Problem 2

Mr. Smith is currently 50 years old and is planning for his retirement. He has been saving $20,000 per year for 20 years, and the current value of his retirement account is $735,712. He plans to make an additional 15 payments of $20,000 each into the retirement plan, retire at age 65 (right after making his last payment), and receive an annual benefit payment (pension) for the following 20 years, i.e., from age 66 to age 85. He expects to earn a return of 6% on his investments while he is working, and then expects to earn 4% a year in retirement. He would like his benefit payments in retirement to be $200,000 per year (with no growth).

(a) How much does Mr. Smith need to have in his account at age 65 (right after making his last payment) to achieve his goal?

(b) At his current rate of savings, how much should He expect to have in his account at age 65 (right after making his last payment)?

(c) At his current rate of savings, how much should He expect his annual benefit payment to be in retirement?