Revision as of 21:29, 18 November 2023 by Admin (Created page with "An investor deposits 225 into a bank at the beginning of each month for 20 years. The bank pays interest at an annual effective rate of 8%. At the end of 20 years, the investor uses the money in the bank to buy a 30-year annuity-due with annual payments of X. These annual payments are based on an annual effective interest rate of 7%. Calculate X. <ul class="mw-excansopts"><li>9,642</li><li>9,704</li><li>9,981</li><li>10,317</li><li>10,383</li></ul> {{soacopyright | 20...")
ABy Admin
Nov 18'23
Exercise
An investor deposits 225 into a bank at the beginning of each month for 20 years. The bank pays interest at an annual effective rate of 8%. At the end of 20 years, the investor uses the money in the bank to buy a 30-year annuity-due with annual payments of X. These annual payments are based on an annual effective interest rate of 7%.
Calculate X.
- 9,642
- 9,704
- 9,981
- 10,317
- 10,383
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: B
[[math]]
\begin{aligned}
& (1+j)^{12}=1.08 \\
& j=0.006434 \\
& 225 \ddot{s}_{\overline{240} \mid 0.006434}=128,848.51 \\
& 128,848.51=X \ddot{a}_{\overline{30} \mid 0.07} \\
& 128,848.51=X(13.27767) \\
& X=9704.15
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.