An investor will accumulate 10,000 at the end of ten years by making level deposits of X at the beginning of each year. The deposits earn 12% simple interest at the end of every year but the interest is reinvested at an annual effective rate of 8%.

Calculate X.

• 508.79
• 541.47
• 569.84
• 597.73
• 608.42

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

Solution: B

The accumulation is

[[math]] 10X+0.12X(Is)_{\overline{10}|0.08}=10X+0.12X{\frac{\ddot{s}_{\overline{10}|0.08}-10}{0.08}}=10X+0.12X{\frac{15.6455-10}{0.08}}=18.4683X [[/math]]

Then, X = 10,000/18.4683 = 541.47

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