An actuary invests 1000 at the end of each year for 30 years. The investments will earn interest at a 4% annual effective interest rate and, at the end of each year, the interest will be reinvested at a 3% annual effective interest rate.

Calculate the accumulated value of the investment at the end of the 30-year period.

• 51,625
• 53,434
• 55,260
• 58,437
• 58,938

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

[[math]] \left[40(I S)_{\overline{29} \mid 0.03}+30(1000)\right]=\left[40 \frac{\ddot{s}_{ \overline{29} \mid 0.03}-29}{0.03}+30(1000)\right]=53,433.89 [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.