Revision as of 20:47, 18 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>2,113</li><li>2,592</li><li>5,958</li><li>9,595</li><li>11,574</li></ul> {{soacopyright |...")
ABy Admin
Nov 18'23
Exercise
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.
ABy Admin
Nov 18'23
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.