You are checking gross premium policy values for a fully discrete whole life insurance of 1000 on (50).

[math]{ }_{k} V[/math] denotes the gross premium policy value at the end of year [math]k, k=0,1,2, \ldots[/math].

The valuation assumptions were intended to include:

i) There are commissions and maintenance expenses payable at the beginning of the year

ii) There are no other expenses

iii) [math]q_{58}=0.002736[/math]

iv) [math]i=0.05[/math]

You discover that all intended assumptions were used correctly, except that calculations were based on [math]q_{58}=0.003736[/math].

The calculated results included [math]{ }_{8} V=86.74[/math] and [math]{ }_{9} V=100[/math].

Calculate [math]{ }_{8} V[/math] using the intended value of [math]q_{58}[/math].

• 85.79
• 85.88
• 85.97
• 86.06
• 86.15

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: B

There is no change to [math]{ }_{9} V[/math] because there were no errors after time 9 .

An equation for [math]{ }_{8} V^{\text {orig }}[/math] is [math]{ }_{8} V^{\text {orig }}+P-e=1000(0.003736) / 1.05+100(0.996264) / 1.05[/math]

An equation for [math]8 V^{\text {now }}[/math] is [math]8 V^{\text {now }}+P-e=1000(0.002736) / 1.05+100(0.997264) / 1.05[/math]

By subtraction, [math]{ }_{8} V^{\text {now }}-{ }_{8} V^{\text {orig }}=1000(-0.001) / 1.05+100(0.001) / 1.05=-0.86[/math]

[math]{ }_{8} V^{\text {now }}=86.74-0.86=85.88(\mathrm{~B})[/math]

In those equations, [math]P-e[/math], which cancels, represents the gross premium less all expenses. You could think of [math]P[/math] as the gross premium less commissions, and e as the flat expenses. However you think of representing them, they cancel.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.