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.

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.