For a fully discrete 30 payment whole life insurance of 1000 on (50) with level annual premiums of [math]16,{ }_{k} V[/math] denotes the gross premium policy value at the end of year [math]k, k=0,1,2, \ldots[/math].

The original valuation assumptions include:

i) Mortality follows the Standard Ultimate Life Table

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

iii) Premium taxes are [math]2 \%[/math]

iv) There are commissions and various other expenses

Using the original valuation assumptions, [math]{ }_{10} V=110[/math].

At some point prior to year 10 , your jurisdiction increased the premium tax rate so the premium tax assumption increased to [math]3 \%[/math]. All other assumptions are unchanged.

Calculate the revised value of [math]{ }_{10} \mathrm{~V}[/math].

• 112
• 114
• 116
• 118
• 120

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

Answer: A

There is no change in the EPV of future benefits or of future gross premiums. Each year that a premium is due, the expense changes by [math](3 \%-2 \%)[/math] of 16 , or 0.16 . Since at the end of year 10 , the insured is 60 with 20 remaining premiums, the EPV of future expense rises by

[math]0.16 \ddot{a}_{60: \overline{20}}=0.16(12.3816)=1.981[/math]

The new reserve is [math]110+1.981=112[/math]

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