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.

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.