Revision as of 18:18, 25 July 2024 by Admin (Created page with "The diagram below describes the rate changes: <div style = "text-align:center;"> {{#invoke_html:actuarial_science/pgram | html | 700 | 300 | 75 | 3 | 9/1/1 | 5/1/2 | 3 | 7}} </div> Using the parallelogram method, the on-level factor for calendar year 2 equals 1.03*1.07, the cumulative rate index, divided by the weighted average index. The weighted average index equals <math display = "block"> A_1 + 1.03\cdot A_2 + 1.03 \cdot 1.07 \cdot A_3 </math> with <math>A_1...")
Exercise
ABy Admin
Jul 25'24
Answer
The diagram below describes the rate changes:
Using the parallelogram method, the on-level factor for calendar year 2 equals 1.03*1.07, the cumulative rate index, divided by the weighted average index. The weighted average index equals
[[math]]
A_1 + 1.03\cdot A_2 + 1.03 \cdot 1.07 \cdot A_3
[[/math]]
with [math]A_1 [/math] the area of region 1 intersected with rectangle CY2, [math]A_2 [/math] the area of region 2 intersected with rectangle CY2 and [math]A_3 [/math] the area of region 3 intersected with rectangle CY3. Elementary geometry implies that [math]A_1 [/math] and [math]A_3[/math] equals
(8/12)2/2 = 0.4444
and [math]A_2 [/math] equals
1-2*0.4444 = 0.1122.
Hence the weighted average index equals
0.4444 + 1.03 * 0.1122 + 1.03 * 1.07 * 0.4444 = 1.0487
, the on-level factor equals
1.03*1.07/1.0487 = 1.05092
, and finally the on-level earned premium equals 10M multiplied by 1.05092 or 10,509,200.