Revision as of 20:45, 18 November 2023 by Admin (Created page with "A payment of 7 is deposited into an account at the end of each year for 45 years. The account earns an annual effective interest rate of i. Immediately after the 45th deposit of 7, the account has accumulated to X, which is used to purchase a perpetuity-immediate. At an annual effective interest rate of 1.2i, the perpetuity will make annual payments of 75.60. Calculate X. <ul class="mw-excansopts"><li>1050</li><li>1120</li><li>1200</li><li>1260</li><li>1340</li></ul>...")
ABy Admin
Nov 18'23
Exercise
A payment of 7 is deposited into an account at the end of each year for 45 years. The account earns an annual effective interest rate of i. Immediately after the 45th deposit of 7, the account has accumulated to X, which is used to purchase a perpetuity-immediate. At an annual effective interest rate of 1.2i, the perpetuity will make annual payments of 75.60.
Calculate X.
- 1050
- 1120
- 1200
- 1260
- 1340
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
[[math]]\begin{aligned} & 7 s_{\overline{45}|i}=\frac{75.6}{1.2 i} \\ & \frac{7\left[(1+i)^{45}-1\right]}{i}=\frac{75.6}{1.2 i} \\ & 7(1+i)^{45}-7=63 \\ & (1+i)^{45}=10 \\ & i=0.0525 \\ & X=7 s_{\overline{45} \mid 0.0525}=1200\end{aligned}[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.