Exercise
For a fully discrete whole life insurance of 1000 on (60), you are given:
i) Reserves are determined using a modified net premium reserve method
ii) The modified reserve at the end of year 2 is 0
iii) Valuation premiums in years 3 and later are level
iv) Mortality follows the Standard Ultimate Life Table v) [math]i=0.05[/math]
Calculate the modified net premium reserve at the end of year 5 .
- 58
- 69
- 79
- 90
- 99
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: A
The policy value at duration 2 is [math]{ }_{2} V^{\mathrm{mod}}=1000 A_{62}-\left(P^{\bmod }\right)\left(\ddot{a}_{62}\right)=0[/math]
[math]P^{\mathrm{mod}}=1000 A_{62} / \ddot{a}_{62}=1000(0.31495) / 14.3861=21.89[/math]
[math]{ }_{5} V^{\mathrm{mod}}=1000 A_{65}-\left(P^{\mathrm{mod}}\right)\left(\ddot{a}_{65}\right)=1000(0.35477)-21.89(13.5498)=58[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.