An investor wants to accumulate 150,000 to purchase a business in ten years. The investor deposits 14,000 into an account at the beginning of each of years one through five. The investor deposits an additional amount X at the beginning of years four and five to meet this goal. The account earns interest at an annual effective rate of 8%.

Calculate X.

• 2,113
• 2,592
• 5,958
• 9,595
• 11,574

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

Solution: C

[[math]] \begin{aligned} & 150,000=\left(14,000 \ddot{s}_{\overline{5}_{0.08}}+X \dot{s}_{\overline{2}|0.08}\right) 1.08^5 \\ & 150,000=(88,703.01+2.2464 X) 1.46933 \\ & X=5,958 \end{aligned} [[/math]]

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