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ABy Admin
Nov 18'23
Exercise
Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The annual nominal interest rate is 9% convertible quarterly.
Calculate X.
- 2680
- 2730
- 2780
- 2830
- 2880
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: B
Convert 9% convertible quarterly to an effective rate of j per month:
[[math]]
(1+j)^{3}=\left(1+{\frac{0.09}{4}}\right)\,{\mathrm{or}}\,j=0.00744.
[[/math]]
Then
[[math]]
2(Ia)_{\overline{60}|0.00744}=2{\frac{\ddot{a}_{\overline{60}|0.00744}-60\nu^{60}}{0.00744}}=2{\frac{48.6136-38.4592}{0.00744}}=2729.7.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.