{"text_format":"1","workbook":"xlsx","n_sheets":5,"sheets":["TOC","1","2","3","4"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"TOC","index":0,"n_rows":6,"n_cols":3,"rows_kept":6,"cut":false,"hidden":false,"merged":[]}
[]
[null,"#","type"]
[null,1," Reserving Methods - FS (Disposal Rate Method)"]
[null,2," Reserving Methods - COS (Case O/S Method #1)"]
[null,3," Reserving Methods - PBS (Paid Berq-Sherm)"]
[null,4," Calculate emergence in a future period"]

{"sheet":"1","index":1,"n_rows":60,"n_cols":28,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["Reading:",null,"Friedland 10 (Frequency-Severity Methods)",null,null,null,null,null,null,null,null,null,null,"|","Step 1a"," calculate CPC and IPC",null,null,"(you will be given 1 of them and have to calculate the other)",null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2019.Fall #20",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Reserving Methods - FS (Disposal Rate Method)",null,null,null,null,null,null,null,null,null,null,"|",null,"given","Cumulative Paid Counts (CPC)",null,null,null,null,null,"Incremental Paid Counts (IPC)",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,"AY",12,24,36,48,null,"|"]
["Find",null,"Use the frequency-severity disposal rate method to estimate",null,null,null,null,null,"unpaid","claims for AY 2025",null,null,null,"|",null,{"$f":"C14","v":2022},{"$f":"D14","v":1590},{"$f":"E14","v":1635},{"$f":"F14","v":1655},{"$f":"G14","v":1671},null,{"$f":"C14","v":2022},{"$f":"Q5","v":1590},{"$f":"R5-Q5","v":45},{"$f":"S5-R5","v":20},{"$f":"T5-S5","v":16},null,"|"]
[null,null,"Random",null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P5+1","v":2023},{"$f":"D15","v":1606.0000000000002},{"$f":"E15","v":1792.0000000000002},{"$f":"F15","v":1840},null,null,{"$f":"V5+1","v":2023},{"$f":"Q6","v":1606.0000000000002},{"$f":"R6-Q6","v":186},{"$f":"S6-R6","v":47.999999999999773},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P6+1","v":2024},{"$f":"D16","v":1605},{"$f":"E16","v":1700},null,null,null,{"$f":"V6+1","v":2024},{"$f":"Q7","v":1605},{"$f":"R7-Q7","v":95},null,null,null,"|"]
["Given",null,"A court ruling on Dec 31, 2025 will increase future claims payments by",null,null,null,null,null,null,0,null,null,null,"|",null,{"$f":"P7+1","v":2025},{"$f":"D17","v":1604},null,null,null,null,{"$f":"V7+1","v":2025},{"$f":"Q8","v":1604},null,null,null,null,"|"]
[null,null,"All claims are closed by 48 months",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"Severity trend:",null,0.03,null,null,null,null,null,null,null,null,"|","Step 1b"," calculate CPL and IPL",null,null,"(you will be given 1 of them and have to calculate the other)",null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,"Cumulative Paid Counts (CPC)",null,null,null,"Ultimate",null,null,null,null,null,"|",null,"given","Cumulative Paid Loss ($000s) (CPL)",null,null,null,null,null,"Incremental Paid Loss ($000s)  (IPL)",null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,"Counts",null,null,null,null,null,"|",null,"AY",12,24,36,48,null,"AY",12,24,36,48,null,"|"]
[null,null,2022,1590,1635,1655,1671,1671,null,null,null,null,null,"|",null,{"$f":"C14","v":2022},{"$f":"D21","v":7001},{"$f":"E21","v":8051},{"$f":"F21","v":8212},{"$f":"G21","v":8212},null,{"$f":"C14","v":2022},{"$f":"Q14","v":7001},{"$f":"R14-Q14","v":1050},{"$f":"S14-R14","v":161},{"$f":"T14-S14","v":0},null,"|"]
[null,null,{"$f":"C14+1","v":2023},1606.0000000000002,1792.0000000000002,1840,null,1951,null,null,null,null,null,"|",null,{"$f":"P14+1","v":2023},{"$f":"D22","v":6998},{"$f":"E22","v":8164},{"$f":"F22","v":8343},null,null,{"$f":"V14+1","v":2023},{"$f":"Q15","v":6998},{"$f":"R15-Q15","v":1166},{"$f":"S15-R15","v":179},null,null,"|"]
[null,null,{"$f":"C15+1","v":2024},1605,1700,null,null,1863,null,null,null,null,null,"|",null,{"$f":"P15+1","v":2024},{"$f":"D23","v":8008},{"$f":"E23","v":9240},null,null,null,{"$f":"V15+1","v":2024},{"$f":"Q16","v":8008},{"$f":"R16-Q16","v":1232},null,null,null,"|"]
[null,null,{"$f":"C16+1","v":2025},1604,null,null,null,1860,null,null,null,null,null,"|",null,{"$f":"P16+1","v":2025},{"$f":"D24","v":6480},null,null,null,null,{"$f":"V16+1","v":2025},{"$f":"Q17","v":6480},null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,"Cumulative Paid Loss ($000s)  (CPL)",null,null,null,null,null,null,null,null,null,"|","Step 2a"," calculate CDR as:",null,"CPC / UC","  (UC = Ultimate Counts)",null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2022,7001,8051,8212,8212,null,null,null,null,null,null,"|",null,null,"Claims DIsposal Rate (CDR)",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C21+1","v":2023},6998,8164,8343,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C22+1","v":2024},8008,9240,null,null,null,null,null,null,null,null,"|",null,{"$f":"C14","v":2022},{"$f":"ROUND(Q5/$H14,3)","v":0.95199999999999996},{"$f":"ROUND(R5/$H14,3)","v":0.97799999999999998},{"$f":"ROUND(S5/$H14,3)","v":0.99},{"$f":"ROUND(T5/$H14,3)","v":1},null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C23+1","v":2025},6480,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P23+1","v":2023},{"$f":"ROUND(Q6/$H15,3)","v":0.82299999999999995},{"$f":"ROUND(R6/$H15,3)","v":0.91900000000000004},{"$f":"ROUND(S6/$H15,3)","v":0.94299999999999995},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P24+1","v":2024},{"$f":"ROUND(Q7/$H16,3)","v":0.86199999999999999},{"$f":"ROUND(R7/$H16,3)","v":0.91300000000000003},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P25+1","v":2025},{"$f":"ROUND(Q8/$H17,3)","v":0.86199999999999999},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"select",{"$f":"ROUND(AVERAGE(Q23:Q26),3)","v":0.875},{"$f":"ROUND(AVERAGE(R23:R26),3)","v":0.93700000000000006},{"$f":"ROUND(AVERAGE(S23:S26),3)","v":0.96699999999999997},{"$f":"ROUND(AVERAGE(T23:T26),3)","v":1},"  <-- default selection  =  all period average",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 2b"," project IPC",null,"(project the Incremental Paid Counts to the lower right portion of the IPC triangle)",null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"Incremental Paid Counts (IPC)",null,null,null,null,"This is the part of the calculation where it's easy to make a",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,"mistake.",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C14","v":2022},null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P33+1","v":2023},null,null,null,{"$f":"Q44","v":111},null,"You have to distribute the remaining counts",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P34+1","v":2024},null,null,{"$f":"Q42","v":78},{"$f":"Q43","v":85.381},null,"proportionately using the disposal rate you selected in the",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P35+1","v":2025},null,{"$f":"Q39","v":127},{"$f":"Q40","v":61},{"$f":"Q41","v":68},null,"previous step.",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,"remaining counts",null,null,"proportional distribution",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"2025/24:",{"$f":"ROUND((H17-Q8)*(R27-Q27)/(T27-Q27),0)","v":127},"=",{"$f":"\"( \"&H17&\" - \"&Q8&\" )\"","v":"( 1860 - 1604 )"},null,"x",{"$f":"\"( \" & R27 & \" - \" & Q27 & \" )\"","v":"( 0.937 - 0.875 )"},null,"/",{"$f":"\"( \" & T27 & \" - \" & Q27 & \" )\"","v":"( 1 - 0.875 )"},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"2025/36:",{"$f":"ROUND((H17-Q8)*(S27-R27)/(T27-Q27),0)","v":61},"=",{"$f":"\"( \"&H17&\" - \"&Q8&\" )\"","v":"( 1860 - 1604 )"},null,"x",{"$f":"\"( \" & S27 & \" - \" & R27 & \" )\"","v":"( 0.967 - 0.937 )"},null,"/",{"$f":"\"( \" & T27 & \" - \" & Q27 & \" )\"","v":"( 1 - 0.875 )"},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"2025/48:",{"$f":"ROUND((H17-Q8)*(T27-S27)/(T27-Q27),0)","v":68},"=",{"$f":"\"( \"&H17&\" - \"&Q8&\" )\"","v":"( 1860 - 1604 )"},null,"x",{"$f":"\"( \" & T27 & \" - \" & S27 & \" )\"","v":"( 1 - 0.967 )"},null,"/",{"$f":"\"( \" & T27 & \" - \" & Q27 & \" )\"","v":"( 1 - 0.875 )"},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","*","2024/36:",{"$f":"ROUND((H16-R7)*(S27-R27)/(T27-R27),0)","v":78},"=",{"$f":"\"( \"&H16&\" - \"&R7&\" )\"","v":"( 1863 - 1700 )"},null,"x",{"$f":"\"( \" & S27 & \" - \" & R27 & \" )\"","v":"( 0.967 - 0.937 )"},null,"/",{"$f":"\"( \" & T27 & \" - \" & R27 & \" )\"","v":"( 1 - 0.937 )"},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","*","2024/48:",{"$f":"ROUND((H16-R7)*(T27-S27)/(T27-R27),3)","v":85.381},"=",{"$f":"\"( \"&H16&\" - \"&R7&\" )\"","v":"( 1863 - 1700 )"},null,"x",{"$f":"\"( \" & T27 & \" - \" & S27 & \" )\"","v":"( 1 - 0.967 )"},null,"/",{"$f":"\"( \" & T27 & \" - \" & R27 & \" )\"","v":"( 1 - 0.937 )"},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","*","2023/48:",{"$f":"ROUND((H15-S6)*(T27-S27)/(T27-S27),0)","v":111},"=",{"$f":"\"( \"&H15&\" - \"&S6&\" )\"","v":"( 1951 - 1840 )"},null,"x",{"$f":"\"( \" & T27 & \" - \" & S27 & \" )\"","v":"( 1 - 0.967 )"},null,"/",{"$f":"\"( \" & T27 & \" - \" & S27 & \" )\"","v":"( 1 - 0.967 )"},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","*","Note that don't have to project every AY. You only have to project the rows for AYs you're asked to calculate.",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3a"," calculate IPS trended to AY 2025, and select an AY 2025 severity for the unpaid periods 24, 36, 48",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"Incremental Paid Severity (IPS)",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,"demonstration of severity calc & trending for age 24",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C14","v":2022},{"$f":"W14/W5*(1+E10)^($P$54-$P51)","v":4.8114350484276729},{"$f":"X14/X5*(1+E10)^($P$54-$P51)","v":25.496963333333333},{"$f":"Y14/Y5*(1+E10)^($P$54-$P51)","v":8.7964523500000009},{"$f":"Z14/Z5*(1+E10)^($P$54-$P51)","v":0},null,{"$f":"R51","v":25.496963333333333},"=",{"$f":"\"( \" & X14&\" / \"&X5&\" )\" & \" x \" & \"( \"&\"1\"& \" + \" & E10*100 & \"% )\" & \"^3\"","v":"( 1050 / 45 ) x ( 1 + 3% )^3"},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P51+1","v":2023},{"$f":"W15/W6*(1+E10)^($P$54-$P52)","v":4.6227759651307583},{"$f":"X15/X6*(1+E10)^($P$54-$P52)","v":6.65058817204301},{"$f":"Y15/Y6*(1+E10)^($P$54-$P52)","v":3.956272916666685},null,null,{"$f":"R52","v":6.65058817204301},"=",{"$f":"\"( \" & X15&\" / \"&X6&\" )\" & \" x \" & \"( \"&\"1\"& \" + \" & E10*100 & \"% )\" & \"^2\"","v":"( 1166 / 186 ) x ( 1 + 3% )^2"},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P52+1","v":2024},{"$f":"W16/W7*(1+E10)^($P$54-$P53)","v":5.1390903426791281},{"$f":"X16/X7*(1+E10)^($P$54-$P53)","v":13.357473684210525},null,null,null,{"$f":"R53","v":13.357473684210525},"=",{"$f":"\"( \" & X16&\" / \"&X7&\" )\" & \" x \" & \"( \"&\"1\"& \" + \" & E10*100 & \"% )\" & \"^1\"","v":"( 1232 / 95 ) x ( 1 + 3% )^1"},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,2025,{"$f":"W17/W8*(1+E10)^($P$54-$P54)","v":4.0399002493765588},{"$f":"ROUND(AVERAGE(R51:R53),3)","v":15.167999999999999},{"$f":"ROUND(AVERAGE(S51:S53),3)","v":6.3760000000000003},{"$f":"ROUND(AVERAGE(T51:T53),3)","v":0},"  <-- default selected severity  =  all period average (except age 12)",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"counts",null,{"$f":"R36","v":127},{"$f":"S36","v":61},{"$f":"T36","v":68},"  <-- from Step 2b",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3b","unpaid",null,{"$f":"R55*R54","v":1926.336},{"$f":"S55*S54","v":388.93600000000004},{"$f":"T55*T54","v":0},"  <-- (selected severity) x counts",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"court ruling adj.",null,{"$f":"J8","v":0},{"$f":"J8","v":0},{"$f":"J8","v":0},"  <-- adjust unpaid by this percentage",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"adj. unpaid",null,{"$f":"R56*(1+R57)","v":1926.336},{"$f":"S56*(1+S57)","v":388.93600000000004},{"$f":"T56*(1+T57)","v":0},{"$f":"SUM(R58:T58)","v":2315.2719999999999},"  <-- final answer for UNPAID loss",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,{"$f":"U58+D24","v":8795.2720000000008},"  <-- ULTIMATE loss",null,null,null,null,null,"|"]
["----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]

{"sheet":"2","index":2,"n_rows":60,"n_cols":28,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["Reading:",null,"Friedland 12 (Case Outstanding Methods)",null,null,null,null,null,null,null,null,null,null,"|","Step 1"," calculate   IPL",null,"(Incremental Paid Loss)",null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2019.Fall #18",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Reserving Methods - COS (Case O/S Method #1)",null,null,null,null,null,null,null,null,null,null,"|",null,null,"Incremental Paid Loss ($000s)  (IPL)",null,null,null,null,"Sometimes you're given the incremental paid loss.",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,"If so, then step 1 is not necessary.",null,null,null,null,null,"|"]
["Find",null,"Use a Case O/S method to calculate the",null,null,null,"ultimate","for AY",2024,null,null,null,null,"|",null,{"$f":"C10","v":2022},{"$f":"D10","v":1608},{"$f":"E10-D10","v":1415},{"$f":"F10-E10","v":892.00000000000045},{"$f":"G10-F10","v":300.99999999999955},null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P5+1","v":2023},{"$f":"D11","v":2358},{"$f":"E11-D11","v":2031},{"$f":"F11-E11","v":1228},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P6+1","v":2024},{"$f":"D12","v":2100},{"$f":"E12-D12","v":1736.0000000000005},null,null,null,null,null,null,null,null,null,"|"]
["Given",null,null,"Cumulative Paid Loss ($000s)  (CPL)",null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7+1","v":2025},{"$f":"D13","v":2414},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2022,1608,3023,3915.0000000000005,4216,null,null,null,null,null,null,"|","Step 2a"," calculate & make selections for:  (current case) / (prior case)",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C10+1","v":2023},2358,4389,5617,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,"Demonstration for AY 2022 calculations:",null,null,null,null,null,"|"]
[null,null,{"$f":"C11+1","v":2024},2100,3836.0000000000005,null,null,null,null,null,null,null,null,"|",null,null,"Current/Prior COS",null,null,null,null,null,null,"current",null,"prior",null,"|"]
[null,null,{"$f":"C12+1","v":2025},2414,null,null,null,null,null,null,null,null,null,"|",null,"AY","24/12","36/24","48/36","60/48",null,null,null,"case O/S",null,"case O/S",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C10","v":2022},{"$f":"IFERROR(ROUND(E17/D17,3),\"\")","v":0.53700000000000003},{"$f":"IFERROR(ROUND(F17/E17,3),\"\")","v":0.504},{"$f":"IFERROR(ROUND(G17/F17,3),\"\")","v":0.40500000000000003},null,"24/12 ",{"$f":"IFERROR(ROUND(X14/Z14,3),\"\")","v":0.53700000000000003},"=",{"$f":"E17","v":1128},"/",{"$f":"D17","v":2100},null,"|"]
[null,null,null,"Case Outstanding ($000s) (COS)",null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P14+1","v":2023},{"$f":"ROUND(E18/D18,3)","v":0.57899999999999996},{"$f":"ROUND(F18/E18,3)","v":0.50700000000000001},null,null,"36/24 ",{"$f":"IFERROR(ROUND(X15/Z15,3),\"\")","v":0.504},"=",{"$f":"F17","v":568},"/",{"$f":"E17","v":1128},null,"|"]
[null,null,"AY",12,24,36,48,null,null,null,null,null,null,"|",null,{"$f":"P15+1","v":2024},{"$f":"ROUND(E19/D19,3)","v":0.56499999999999995},null,null,null,"48/36 ",{"$f":"IFERROR(ROUND(X16/Z16,3),\"\")","v":0.40500000000000003},"=",{"$f":"G17","v":230},"/",{"$f":"F17","v":568},null,"|"]
[null,null,2022,2100,1128,568,230,null,null,null,null,null,null,"|",null,{"$f":"P16+1","v":2025},{"$f":"IFERROR(ROUND(AVERAGE(Q14:Q16),3),0)","v":0.56000000000000005},{"$f":"IFERROR(ROUND(AVERAGE(R14:R16),3),0)","v":0.50600000000000001},{"$f":"IFERROR(ROUND(AVERAGE(S14:S16),3),0)","v":0.40500000000000003},{"$f":"IFERROR(ROUND(AVERAGE(T14:T16),3),0)","v":0},"  <-- default selection  =  all period average",null,null,null,null,null,null,"|"]
[null,null,{"$f":"C17+1","v":2023},2840,1645,834,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C18+1","v":2024},2538,1433,null,null,null,null,null,null,null,null,"|","Step 2b"," project case O/S using selections from step 2a",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C19+1","v":2025},3300,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"projected Case Outstanding (COS)",null,null,null,null,"Demonstration for AY 2025 projections:",null,null,null,null,null,"|"]
[null,null,"48-ultimate paid loss to prior case O/S factor",null,null,null,null,1.1000000000000001,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,null,null,null,null,"prior",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C10","v":2022},null,null,null,{"$f":"G17","v":230},null,"projection",null,"selection",null,"case O/S",null,"|"]
[null,null,"* no development past 60 months",null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P23+1","v":2023},null,null,{"$f":"F18","v":834},{"$f":"S24*S17","v":337.77000000000004},"24 mths ",{"$f":"ROUND(X24*Z24,0)","v":1848},"=",{"$f":"Q17","v":0.56000000000000005},"x",{"$f":"Q26","v":3300},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P24+1","v":2024},null,{"$f":"E19","v":1433},{"$f":"ROUND(R25*R17,0)","v":725},{"$f":"ROUND(S25*S17,0)","v":294},"36 mths ",{"$f":"ROUND(X25*Z25,0)","v":935},"=",{"$f":"R17","v":0.50600000000000001},"x",{"$f":"R26","v":1848},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P25+1","v":2025},{"$f":"D20","v":3300},{"$f":"ROUND(Q26*Q17,0)","v":1848},{"$f":"ROUND(R26*R17,0)","v":935},{"$f":"ROUND(S26*S17,0)","v":379},"48 mths ",{"$f":"ROUND(X26*Z26,0)","v":379},"=",{"$f":"S17","v":0.40500000000000003},"x",{"$f":"S26","v":935},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3a"," calculate & make selections for:  (current IPL) / (prior case)",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,"Demonstration for AY 2022 calculations:",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"IPL / (prior case)",null,null,null,null,null,null,"current",null,"prior",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","24/12","36/24","48/36","60/48",null,null,null,"IPL",null,"case O/S",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C10","v":2022},{"$f":"IFERROR(R5/D17,\"\")","v":0.67380952380952386},{"$f":"IFERROR(S5/E17,\"\")","v":0.79078014184397205},{"$f":"IFERROR(T5/F17,\"\")","v":0.52992957746478797},null,"24/12 ",{"$f":"IFERROR(ROUND(X32/Z32,3),\"\")","v":0.67400000000000004},"=",{"$f":"R5","v":1415},"/",{"$f":"D17","v":2100},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P32+1","v":2023},{"$f":"R6/D18","v":0.71514084507042253},{"$f":"S6/E18","v":0.74650455927051673},null,null,"36/24 ",{"$f":"IFERROR(ROUND(X33/Z33,3),\"\")","v":0.79100000000000004},"=",{"$f":"S5","v":892.00000000000045},"/",{"$f":"E17","v":1128},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P33+1","v":2024},{"$f":"R7/D19","v":0.68400315208825868},null,null,null,"48/36 ",{"$f":"IFERROR(ROUND(X34/Z34,3),\"\")","v":0.53},"=",{"$f":"T5","v":300.99999999999955},"/",{"$f":"F17","v":568},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P34+1","v":2025},{"$f":"IFERROR(ROUND(AVERAGE(Q32:Q34),3),1)","v":0.69099999999999995},{"$f":"IFERROR(ROUND(AVERAGE(R32:R34),3),1)","v":0.76900000000000002},{"$f":"IFERROR(ROUND(AVERAGE(S32:S34),3),1)","v":0.53},null,"  <-- default selection  =  all period average",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3b"," project IPL using selections from step 3a",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,"Demonstration for AY 2025 projections:",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"projected Incremental Paid Loss (IPL)",null,null,null,null,null,null,null,null,null,"prior","|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,60,null,"projection",null,"selection *",null,"case O/S","|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C10","v":2022},null,null,null,null,{"$f":"H22*T23","v":253.00000000000003},"24 mths ",{"$f":"ROUND(Y41*AA41,0)","v":2280},"=",{"$f":"Q35","v":0.69099999999999995},"x",{"$f":"Q26","v":3300},"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P41+1","v":2023},null,null,null,{"$f":"ROUND(S35*S24,0)","v":442},{"$f":"ROUND(H22*T24,0)","v":372},"36 mths ",{"$f":"ROUND(Y42*AA42,0)","v":1421},"=",{"$f":"R35","v":0.76900000000000002},"x",{"$f":"R26","v":1848},"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P42+1","v":2024},null,null,{"$f":"ROUND(R35*R25,0)","v":1102},{"$f":"ROUND(S35*S25,0)","v":384},{"$f":"ROUND(H22*T25,0)","v":323},"48 mths ",{"$f":"ROUND(Y43*AA43,0)","v":496},"=",{"$f":"S35","v":0.53},"x",{"$f":"S26","v":935},"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P43+1","v":2025},null,{"$f":"ROUND(Q35*Q26,0)","v":2280},{"$f":"ROUND(R35*R26,0)","v":1421},{"$f":"ROUND(S35*S26,0)","v":496},{"$f":"T26*H22","v":416.90000000000003},"60 mths ",{"$f":"ROUND(Y44*AA44,0)","v":417},"=",{"$f":"H22","v":1.1000000000000001},"x",{"$f":"T26","v":379},"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"Note:","The IPL projection always has 1 extra column. In this",null,null,null,null,null,"* The 60-mth selection was given info.",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"case 60-months. We use the 48-month case O/S",null,null,null,null,null,"   (It was not selected in step 3a)",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"to project the IPL out to 60 months.",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Final"," calculate ultimate & unpaid amounts:",null,null,null," unpaid","=","sum of rows in step 3b",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null," ultimate","=","sum of rows in step 3b    +     last diagonal of CPL",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","ultimate","unpaid",null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C10","v":2022},{"$f":"SUM(Q5:T5)+SUM(Q41:U41)","v":4469},{"$f":"SUM(Q41:U41)","v":253.00000000000003},null,"Pay attention to whether the question asks for ultimate or unpaid.",null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P54+1","v":2023},{"$f":"SUM(Q6:T6)+SUM(Q42:U42)","v":6431},{"$f":"SUM(Q42:U42)","v":814},null,"Also, pay attention to which AY is being asked about.",null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P55+1","v":2024},{"$f":"SUM(Q7:T7)+SUM(Q43:U43)","v":5645},{"$f":"SUM(Q43:U43)","v":1809},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P56+1","v":2025},{"$f":"SUM(Q8:T8)+SUM(Q44:U44)","v":7027.9},{"$f":"SUM(Q44:U44)","v":4613.8999999999996},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"The final",{"$f":"G5","v":"ultimate"},"for AY",{"$f":"I5","v":2024},"is",{"$f":"VLOOKUP(S59,P54:R57,IF(Q59=\"ultimate\",2,3),FALSE)","v":5645}," <-- final answer",null,null,null,null,null,"|"]
["----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]

{"sheet":"3","index":3,"n_rows":60,"n_cols":39,"rows_kept":60,"cut":false,"hidden":false,"merged":[[22,31,22,32],[22,33,22,34],[22,35,22,36],[22,37,22,38],[22,3,22,4],[22,5,22,6],[22,7,22,8],[22,9,22,10],[22,11,22,12],[22,29,22,30]]}
["Reading:",null,"Friedland 13 (Berquist-Sherman Methods)",null,null,null,null,null,null,null,null,null,null,"|","Step 1a"," calculate CDR as:",null,"CPC / UC","  (UC = Ultimate Counts)",null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2016.Spring #20",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Reserving Methods - PBS (Paid Berq-Sherm)",null,null,null,null,null,null,null,null,null,null,"|",null,null,"Claims DIsposal Rate (CDR)",null,null,null,null,"We assume the latest diagonal reflects current",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,"disposal rates. (This is the most recent CY.)",null,null,null,null,null,"|"]
["Find",null,"Use the paid Berquist-Sherman method to calculate the",null,null,null,null,null,"unpaid","for AY",2025,null,null,"|",null,{"$f":"C10","v":2022},{"$f":"IFERROR(ROUND(D10/H10,3),\"\")","v":0.95199999999999996},{"$f":"IFERROR(ROUND(E10/H10,3),\"\")","v":0.97799999999999998},{"$f":"IFERROR(ROUND(F10/H10,3),\"\")","v":0.99},{"$f":"IFERROR(ROUND(G10/H10,3),\"\")","v":1},null,"We will restate all AYs to be at the level of this",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P5+1","v":2023},{"$f":"ROUND(D11/H11,3)","v":0.86399999999999999},{"$f":"ROUND(E11/H11,3)","v":0.96499999999999997},{"$f":"ROUND(F11/H11,3)","v":0.99},null,null,"most recent CY.",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P6+1","v":2024},{"$f":"ROUND(D12/H12,3)","v":0.90500000000000003},{"$f":"ROUND(E12/H12,3)","v":0.95799999999999996},null,null,null,null,null,null,null,null,null,"|"]
["Given",null,null,"Cumulative Paid Counts (CPC)",null,null,null,"Ultimate",null,"* May be development past 48 months",null,null,null,"|",null,{"$f":"P7+1","v":2025},{"$f":"ROUND(D13/H13,3)","v":0.90500000000000003},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,"Counts",null,null,null,null,null,"|",null,"last CY",{"$f":"Q8","v":0.90500000000000003},{"$f":"R7","v":0.95799999999999996},{"$f":"S6","v":0.99},{"$f":"T5","v":1},"  <-- select LATEST DIAGONAL (not all-period-average)",null,null,null,null,null,null,"|"]
[null,null,2022,1590,1635,1655,1671,1671,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C10+1","v":2023},1606.0000000000002,1792.0000000000002,1840,null,1857.7885196374625,null,null,null,null,null,"|","Step 1b"," restate CPC using CDRs from last CY",null,null,null,null,null,"This \"range\" table is just a visual aid",null,null,null,null,null,"|"]
[null,null,{"$f":"C11+1","v":2024},1605,1700,null,null,1773.9459068489755,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C12+1","v":2025},1604,null,null,null,1771.7608171925742,null,null,null,null,null,"|",null,null,"Restated Cumulative Paid Counts (CPC)",null,null,null,"===>",null,"Range Relative to Original Paid Counts",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,"AY",12,24,36,48,null,"|"]
[null,null,null,"Cumulative Paid Loss ($000s)  (CPL)",null,null,null,null,"* May be development past 48 months",null,null,null,null,"|",null,{"$f":"C20","v":2025},{"$f":"ROUND(H10*Q9,0)","v":1512},{"$f":"ROUND(H10*R9,0)","v":1601},{"$f":"ROUND(H10*S9,0)","v":1654},{"$f":"ROUND(H10*T9,0)","v":1671},null,{"$f":"C10","v":2022},{"$f":"IF(Q15<D10,\"0-\"&D9,D9&\"-\"&E9)","v":"0-12"},{"$f":"IF(R15<E10,D9&\"-\"&E9,E9&\"-\"&F9)","v":"12-24"},{"$f":"IF(S15<F10,E9&\"-\"&F9,F9&\"-\"&G9)","v":"24-36"},{"$f":"IF(T15<G10,F9&\"-\"&G9,G9&\"-60\")","v":"48-60"},null,"|"]
[null,null,"AY",12,24,36,48,null,null,null,null,null,null,"|",null,{"$f":"P15+1","v":2026},{"$f":"ROUND(H11*Q9,0)","v":1681},{"$f":"ROUND(H11*R9,0)","v":1780},{"$f":"ROUND(H11*S9,0)","v":1839},null,null,{"$f":"V15+1","v":2023},{"$f":"IF(Q16<D11,\"0-\"&D9,D9&\"-\"&E9)","v":"12-24"},{"$f":"IF(R16<E11,D9&\"-\"&E9,E9&\"-\"&F9)","v":"12-24"},{"$f":"IF(S16<F11,E9&\"-\"&F9,F9&\"-\"&G9)","v":"24-36"},null,null,"|"]
[null,null,2022,7001,8051,8212,8212,null,null,null,null,null,null,"|",null,{"$f":"P16+1","v":2027},{"$f":"ROUND(H12*Q9,0)","v":1605},{"$f":"ROUND(H12*R9,0)","v":1699},null,null,null,{"$f":"V16+1","v":2024},{"$f":"IF(Q17<D12,\"0-\"&D9,D9&\"-\"&E9)","v":"12-24"},{"$f":"IF(R17<E12,D9&\"-\"&E9,E9&\"-\"&F9)","v":"12-24"},null,null,null,"|"]
[null,null,{"$f":"C17+1","v":2023},6998,8164,8343,null,null,null,null,null,null,null,"|",null,{"$f":"P17+1","v":2028},{"$f":"ROUND(H13*Q9,0)","v":1603},null,null,null,null,{"$f":"V17+1","v":2025},{"$f":"IF(Q18<D13,\"0-\"&D9,D9&\"-\"&E9)","v":"0-12"},null,null,null,null,"|"]
[null,null,{"$f":"C18+1","v":2024},8008,9240,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C19+1","v":2025},6480,null,null,null,null,null,null,null,null,null,"|",null,"Ex:",{"$f":"Q15","v":1512},"=",{"$f":"Q9&\" x \"&H10","v":"0.905 x 1671"},null,null,"The range table is helpful in visualizing which data points",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"Ex:",{"$f":"R16","v":1780},"=",{"$f":"R9&\" x \"&H11","v":"0.958 x 1857.78851963746"},null,null,"and/or which regression parameters to use in Step 2.",null,null,null,null,null,"|"]
[null,null,null,"parameters for 2-point exponential fit:   y = aebx",null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"parameters for 2-point exponential fit:   y = aebx"]
[null,null,null,"0 - 12",null,"12 - 24",null,"24 - 36",null,"36 - 48",null,"48 - 60",null,"|","Step 2"," restate CPL using linear interpolation",null,null,null,null,"or…"," restate CPL using exponential regression interpolation",null,null,null,null,null,"|",null,"0 - 12",null,"12 - 24",null,"24 - 36",null,"36 - 48",null,"48 - 60"]
[null,null,"AY","a","b","a","b","a","b","a","b","a","b","|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|","AY","1 + b","a","1 + b","a","1 + b","a","1 + b","a","1 + b","a"]
[null,null,2022,"use 12 - 24 values",null,{"$f":"ROUND(AG25,0)","v":50},{"$f":"ROUND(AF25-1,5)","v":3.1099999999999999E-3},{"$f":"ROUND(AI25,0)","v":1595},{"$f":"ROUND(AH25-1,5)","v":9.8999999999999999E-4},{"$f":"ROUND(AK25,0)","v":8212},{"$f":"ROUND(AJ25-1,5)","v":0},"not needed",null,"|",null,null,"Restated Cumulative Paid Loss  (CPL)",null,null,null,null,null,"Restated Cumulative Paid Loss  (CPL)",null,null,null,null,"|",2022,"use 12 - 24 values",null,{"$f":"LOGEST(D17:E17,D10:E10,1,1)","v":1.0031102336894178},50.209852626781242,{"$f":"LOGEST(E17:F17,E10:F10,1,1)","v":1.0009904998131995},1595.4097894004378,{"$f":"LOGEST(F17:G17,F10:G10,1,1)","v":1},8212.0000000000036,"not needed"]
[null,null,{"$f":"C25+1","v":2023},"use 12 - 24 values",null,{"$f":"ROUND(AG26,0)","v":1850},{"$f":"ROUND(AF26-1,5)","v":8.3000000000000001E-4},{"$f":"ROUND(AI26,0)","v":3633},{"$f":"ROUND(AH26-1,5)","v":4.4999999999999999E-4},null,null,null,null,"|",null,"AY",12,24,36,48,null,"AY",12,24,36,48,null,"|",{"$f":"AC25+1","v":2023},"use 12 - 24 values",null,{"$f":"LOGEST(D18:E18,D11:E11,1,1)","v":1.000828890926402},1849.6140038941624,{"$f":"LOGEST(E18:F18,E11:F11,1,1)","v":1.0004519483264744},3632.8802948929092]
[null,null,{"$f":"C26+1","v":2024},"use 12 - 24 values",null,{"$f":"ROUND(AG27,0)","v":714},{"$f":"ROUND(AF27-1,5)","v":1.5100000000000001E-3},null,null,null,null,null,null,"|",null,2022,{"$f":"ROUND(IF(RIGHT(W15,2)=RIGHT(W14,2),(Q15-0)/(D10-0)*(D17-0)+0,(Q15-D10)/(E10-D10)*(E17-D17-0)+D17),0)","v":6658},{"$f":"ROUND(IF(RIGHT(X15,2)=RIGHT(X14,2),(R15-D10)/(E10-D10)*(E17-D17)+D17,(R15-E10)/(F10-E10)*(F17-E17)+E17),0)","v":7258},{"$f":"ROUND(IF(RIGHT(Y15,2)=RIGHT(Y14,2),(S15-E10)/(F10-E10)*(F17-E17)+E17,(S15-F10)/(G10-F10)*(G17-F17)+F17),0)","v":8204},{"$f":"ROUND(G17,0)","v":8212},null,2022,{"$f":"ROUND(IF(RIGHT(W15,2)=RIGHT(W14,2),F25*EXP(G25*Q15),F25*EXP(G25*Q15)),0)","v":5510},{"$f":"ROUND(IF(RIGHT(X15,2)=RIGHT(X14,2),F25*EXP(G25*R15),H25*EXP(I25*R15)),0)","v":7267},{"$f":"ROUND(IF(RIGHT(Y15,2)=RIGHT(Y14,2),H25*EXP(I25*S15),J25*EXP(K25*S15)),0)","v":8202},{"$f":"ROUND(G17,0)","v":8212},null,"|",{"$f":"AC26+1","v":2024},"use 12 - 24 values",null,{"$f":"LOGEST(D19:E19,D12:E12,1,1)","v":1.0015074597467672},713.75889682959019]
[null,null,{"$f":"C27+1","v":2025},"use 12 - 24 values",null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P27+1","v":2023},{"$f":"ROUND(IF(RIGHT(W16,2)=RIGHT(W14,2),(Q16-0)/(D11-0)*(D18-0)+0,(Q16-D11)/(E11-D11)*(E18-D18-0)+D18),0)","v":7468},{"$f":"ROUND(IF(RIGHT(X16,2)=RIGHT(X14,2),(R16-D11)/(E11-D11)*(E18-D18)+D18,(R16-E11)/(F11-E11)*(F18-E18)+E18),0)","v":8089},{"$f":"ROUND(F18,0)","v":8343},null,null,{"$f":"V27+1","v":2023},{"$f":"ROUND(IF(RIGHT(W16,2)=RIGHT(W14,2),F26*EXP(G26*Q16),F26*EXP(G26*Q16)),0)","v":7466},{"$f":"ROUND(IF(RIGHT(X16,2)=RIGHT(X14,2),F26*EXP(G26*R16),H26*EXP(I26*R16)),0)","v":8106},{"$f":"ROUND(F18,0)","v":8343},null,null,"|",{"$f":"AC27+1","v":2025},"use 12 - 24 values"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P28+1","v":2024},{"$f":"ROUND(IF(RIGHT(W17,2)=RIGHT(W14,2),(Q17-0)/(D12-0)*(D19-0)+0,(Q17-D12)/(E12-D12)*(E19-D19-0)+D19),0)","v":8008},{"$f":"ROUND(E19,0)","v":9240},null,null,null,{"$f":"V28+1","v":2024},{"$f":"ROUND(IF(RIGHT(W17,2)=RIGHT(W14,2),F27*EXP(G27*Q17),F27*EXP(G27*Q17)),0)","v":8058},{"$f":"ROUND(E19,0)","v":9240},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P29+1","v":2025},{"$f":"ROUND(D20,0)","v":6480},null,null,null,null,{"$f":"V29+1","v":2025},{"$f":"ROUND(D20,0)","v":6480},null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Exs:",null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"Q27","v":6658},{"$f":"IF(RIGHT(W15,2)=RIGHT(W14,2),\"= (\"&Q15&\"-0)/(\"&D10&\"-0)x(\"&D17&\"-0)+0\",\"= (\"&Q15&\"-\"&D10&\")/(\"&E10&\"-\"&D10&\")x(\"&E17&\"-\"&D17&\")+\"&D17)","v":"= (1512-0)/(1590-0)x(7001-0)+0"},null,null,null,null,null,{"$f":"W27","v":5510},{"$f":"IF(RIGHT(W15,2)=RIGHT(W14,2),\"= \"&F25&\" x EXP(\"&G25&\" x \"&Q15&\")\",\"= \"&F25&\" x EXP(\"&G25&\" x \"&Q15&\")\")","v":"= 50 x EXP(0.00311 x 1512)"},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"R28","v":8089},{"$f":"IF(RIGHT(X16,2)=RIGHT(X14,2),\"= (\"&R16&\"-\"&D11&\")/(\"&E11&\"-\"&D11&\")x(\"&E18&\"-\"&D18&\")+\"&D18,\"= (\"&R16&\"-\"&E11&\")/(\"&F11&\"-\"&E11&\")x(\"&F18&\"-\"&E18&\")+\"&E18)","v":"= (1780-1606)/(1792-1606)x(8164-6998)+6998"},null,null,null,null,null,{"$f":"X28","v":8106},{"$f":"IF(RIGHT(X16,2)=RIGHT(X14,2),\"= \"&F26&\" x \"& \"EXP(\"&G26&\" x \"&R16&\")\",\"= \"&H26&\" x \"&\"EXP(\"&I26&\" x \"&R16&\")\")","v":"= 1850 x EXP(0.00083 x 1780)"},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"S27","v":8204},{"$f":"IF(RIGHT(Y15,2)=RIGHT(Y14,2),\"= (\"&S15&\"-\"&E10&\")/(\"&F10&\"-\"&E10&\")x(\"&F17&\"-\"&E17&\")+\"&E17,\"= (\"&S15&\"-\"&F10&\")/(\"&G10&\"-\"&F10&\")x(\"&G17&\"-\"&F17&\")+\"&F17)","v":"= (1654-1635)/(1655-1635)x(8212-8051)+8051"},null,null,null,null,null,{"$f":"Y27","v":8202},{"$f":"IF(RIGHT(Y15,2)=RIGHT(Y14,2),\"= \"&H25&\" x EXP(\"&I25&\" x \"&S15&\")\",\"= \"&J25&\" x EXP(\"&K25&\" x \"&S15&\")\")","v":"= 1595 x EXP(0.00099 x 1654)"},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3a"," apply development method to restated CPL",null,null,null,null,null," apply development method to restated CPL",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","LDFs","AY",{"$f":"D9&\"-\"&E9","v":"12-24"},{"$f":"E9&\"-\"&F9","v":"24-36"},{"$f":"F9&\"-\"&G9","v":"36-48"},"48-ult","or…","AY",{"$f":"Q38","v":"12-24"},{"$f":"R38","v":"24-36"},{"$f":"S38","v":"36-48"},"48-ult",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C10","v":2022},{"$f":"IFERROR(ROUND(R27/Q27,3),\"\")","v":1.0900000000000001},{"$f":"IFERROR(ROUND(S27/R27,3),\"\")","v":1.1299999999999999},{"$f":"IFERROR(ROUND(T27/S27,3),\"\")","v":1.0009999999999999},null,null,{"$f":"P39","v":2022},{"$f":"IFERROR(ROUND(X27/W27,3),\"\")","v":1.319},{"$f":"IFERROR(ROUND(Y27/X27,3),\"\")","v":1.129},{"$f":"IFERROR(ROUND(Z27/Y27,3),\"\")","v":1.0009999999999999},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P39+1","v":2023},{"$f":"IFERROR(ROUND(R28/Q28,3),\"\")","v":1.083},{"$f":"IFERROR(ROUND(S28/R28,3),\"\")","v":1.0309999999999999},null,null,null,{"$f":"V39+1","v":2023},{"$f":"IFERROR(ROUND(X28/W28,3),\"\")","v":1.0860000000000001},{"$f":"IFERROR(ROUND(Y28/X28,3),\"\")","v":1.0289999999999999},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P40+1","v":2024},{"$f":"IFERROR(ROUND(R29/Q29,3),\"\")","v":1.1539999999999999},null,{"$f":"IFERROR(ROUND(T29/S29,3),\"\")","v":""},"tail",null,{"$f":"V40+1","v":2024},{"$f":"IFERROR(ROUND(X29/W29,3),\"\")","v":1.147},null,{"$f":"IFERROR(ROUND(Z29/Y29,3),\"\")","v":""},"tail",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P41+1","v":2025},null,{"$f":"IFERROR(ROUND(S30/R30,3),\"\")","v":""},{"$f":"IFERROR(ROUND(T30/S30,3),\"\")","v":""},"factor:",null,{"$f":"V41+1","v":2025},null,{"$f":"IFERROR(ROUND(Y30/X30,3),\"\")","v":""},{"$f":"IFERROR(ROUND(Z30/Y30,3),\"\")","v":""},"factor:",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"selected",{"$f":"AVERAGE(Q39:Q41)","v":1.109},{"$f":"AVERAGE(R39:R41)","v":1.0804999999999998},{"$f":"AVERAGE(S39:S41)","v":1.0009999999999999},{"$f":"SQRT(S43)","v":1.000499875062461},null,"selected",{"$f":"AVERAGE(W39:W41)","v":1.1840000000000002},{"$f":"AVERAGE(X39:X41)","v":1.079},{"$f":"AVERAGE(Y39:Y41)","v":1.0009999999999999},{"$f":"SQRT(Y43)","v":1.000499875062461},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","CDFs",null,{"$f":"Q38","v":"12-24"},{"$f":"R38","v":"24-36"},{"$f":"S38","v":"36-48"},{"$f":"T38","v":"48-ult"},null,null,{"$f":"W38","v":"12-24"},{"$f":"X38","v":"24-36"},{"$f":"Y38","v":"36-48"},{"$f":"Z38","v":"48-ult"},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"age -> ult",{"$f":"R46*Q43","v":1.200072361028073},{"$f":"S46*R43","v":1.0821211551199936},{"$f":"T46*S43","v":1.0015003749375233},{"$f":"T43","v":1.000499875062461},null,"age -> ult",{"$f":"X46*W43","v":1.2794527829961839},{"$f":"Y46*X43","v":1.0806189045575876},{"$f":"Z46*Y43","v":1.0015003749375233},{"$f":"Z43","v":1.000499875062461},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Ults.",null,{"$f":"\"'\"&RIGHT(C13,2)&\"@\"&D9","v":"'25@12"},{"$f":"\"'\"&RIGHT(C12,2)&\"@\"&E9","v":"'24@24"},{"$f":"\"'\"&RIGHT(C11,2)&\"@\"&F9","v":"'23@36"},{"$f":"\"'\"&RIGHT(C10,2)&\"@\"&G9","v":"'22@48"},null,null,{"$f":"Q48","v":"'25@12"},{"$f":"R48","v":"'24@24"},{"$f":"S48","v":"'23@36"},{"$f":"T48","v":"'22@48"},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"diagonal",{"$f":"Q30","v":6480},{"$f":"R29","v":9240},{"$f":"S28","v":8343},{"$f":"T27","v":8212},null,"diagonal",{"$f":"W30","v":6480},{"$f":"X29","v":9240},{"$f":"Y28","v":8343},{"$f":"Z27","v":8212},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"ultimate",{"$f":"Q49*Q46","v":7776.4688994619128},{"$f":"R49*R46","v":9998.7994733087417},{"$f":"S49*S46","v":8355.5176281037566},{"$f":"T49*T46","v":8216.1049740129292},null,"ultimate",{"$f":"W49*W46","v":8290.8540338152725},{"$f":"X49*X46","v":9984.9186781121098},{"$f":"Y49*Y46","v":8355.5176281037566},{"$f":"Z49*Z46","v":8216.1049740129292},null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3b",{"$f":"I5","v":"unpaid"},"for AY",2025,"=",{"$f":"ROUND(INDEX(Q50:T50,1,2026-R52)-IF(P52=\"ultimate\",0,INDEX(D17:G20,R52-2021,2026-R52)),0)","v":1296}," <-- estimate based on LINEAR INTERPOLATION",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P52","v":"unpaid"},"for AY",2025,"=",{"$f":"ROUND(INDEX(W50:Z50,1,2026-R53)-IF(P52=\"ultimate\",0,INDEX(D17:G20,R53-2021,2026-R53)),0)","v":1811}," <-- estimate based on EXPONENTIAL REGRESSION INTERPOLATION",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3c","The estimate of ultimate using exponential regression differs from the estimate using liner interpolation by:",null,null,null,null,null,null,null,null,null,null,{"$f":"(T53-T52)/T52","v":0.39737654320987653},"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"(Step 3c was just for fun to see if there is any real difference between linear and exponential interpolation.)",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]

{"sheet":"4","index":4,"n_rows":60,"n_cols":28,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["Reading:",null,"Friedland 15 (Evaluating Methods)",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"Emergence Patterns",null,null,null,null,null,null,null,null,null,null,"|","Step 1"," determine the 12-month period containing the period you're given",null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Calculate emergence in a future period",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"period",{"$f":"J5","v":15},"to",{"$f":"L5","v":21},"is contained in period",null,null,{"$f":"F10","v":12},"to",{"$f":"W4+12","v":24},null,null,"|"]
["Find",null,"Calculate the emergence of",null,null,"paid","claims","in the period",null,15,"to",21,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 2"," calculate the quantites required in the emergence formula (for step 3)",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Given",null,"Here is the current information for a particular AY:",null,null,null,null,null,null,null,null,null,null,"|",null,"ultimate",null,"=",{"$f":"\"paid @\"&F10","v":"paid @12"},"x",{"$f":"W4& \"-ultimate CDF\"","v":"12-ultimate CDF"},null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"H10","v":5020},"x",{"$f":"VLOOKUP(F10,C12:F17,4,FALSE)","v":2.86},null,null,null,null,null,null,"|"]
[null,null,"paid","claims","at",12,"months",5020,null,null,null,null,null,"|",null,null,null,"=",{"$f":"ROUND(S9*U9,0)","v":14357},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,12,"- ultimate"," CDF",2.86,null,null,null,null,null,null,null,"|",null,{"$f":"\"unpaid @ \"&F10","v":"unpaid @ 12"},null,"=","ultimate","-",{"$f":"\"paid @\"&F10","v":"paid @12"},null,null,null,null,null,null,"|"]
[null,null,24,"- ultimate"," CDF",1.47,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S10","v":14357},"-",{"$f":"H10","v":5020},null,null,null,null,null,null,"|"]
[null,null,36,"- ultimate"," CDF",1.1100000000000001,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S13-U13","v":9337},null,null,null,null,null,null,null,null,"|"]
[null,null,48,"- ultimate"," CDF",1.06,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,60,"- ultimate"," CDF",1.03,null,null,null,null,null,null,null,"|",null,{"$f":"\"%paid @ \"&F10","v":"%paid @ 12"},null,"=",1,"/",{"$f":"W4& \"-ultimate CDF\"","v":"12-ultimate CDF"},null,null,null,null,null,null,"|"]
[null,null,72,"- ultimate"," CDF",1.02,null,null,null,null,null,null,null,"|",null,null,null,"=",1,"/",{"$f":"U9","v":2.86},null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S17/U17","v":0.34965034965034969},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"\"%paid @ \"&Y4","v":"%paid @ 24"},null,"=",1,"/",{"$f":"Y4& \"-ultimate CDF\"","v":"24-ultimate CDF"},null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",1,"/",{"$f":"VLOOKUP(Y4,C12:F17,4,FALSE)","v":1.47},null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S21/U21","v":0.68027210884353739},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"\"%unpaid @ \"&F10","v":"%unpaid @ 12"},null,"=",1,"-",{"$f":"\"%paid @ \"&F10","v":"%paid @ 12"},null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",1,"-",{"$f":"S18","v":0.34965034965034969},null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S25-U25","v":0.65034965034965031},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3"," calculate the emergence in the 12-month period using the results from step 2",null,null,null,null,null,null,null,null,null,null,null,"|"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"12-mth emergence",null,"=",{"$f":"P12&\" x ( \"&P20&\" - \"&P16&\" )  /  (\"&P24&\" )\"","v":"unpaid @ 12 x ( %paid @ 24 - %paid @ 12 )  /  (%unpaid @ 12 )"},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S14","v":9337},"x        ( ",{"$f":"S22","v":0.68027210884353739},"-",{"$f":"S18","v":0.34965034965034969}," )        /",{"$f":"S26","v":0.65034965034965031},null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S31*(U31-W31)/Y31","v":4746.7010460098008},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 4"," if the given period was NOT a 12-month interval then you must interpolate to get the final answer",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"given period      =========>",null,null,{"$f":"Q4","v":15},"to",{"$f":"S4","v":21},"which is ",{"$f":"U36-S36","v":6},"months",null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"W36&\"-mth emergence\"","v":"6-mth emergence"},null,"=",{"$f":"S32","v":4746.7010460098008},"x",{"$f":"W36","v":6},"/",12,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,"=",{"$f":"S38*U38/W38","v":2373.3505230049004}," <== final answer",null,null,null,null,null,null,null,"|"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
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