Upon graduating from college 35 years ago, Dr. Nick Riviera was already thinking

Question

Upon graduating from college 35 years ago, Dr. Nick Riviera was already thinking of retirement. Since then he has made deposits into his retirement fund on a quarterly basis in the amount of $300. Nick has just completed his final payment and is at last ready to retire. Additionally, an uncle died 15 years ago and Nick received a check of $20,000 at that time. He deposited the entire amount into his retirement fund.

If Nick expects to live for 20 more years, how much will his quarterly income be during his retirement? His retirement fund has earned 9% compounded quarterly. This rate of return is expected to continue.

Explanation / Answer

Dr. Nick has following total amount in his retirement fund

=300(((1+.09/4)^35*4)/.09/4)+20000(1+.09/4)^20*15*4

= 300(957.1267)+20000(3.8001)

=287138.02+76002.70

=$ 363,140.72

To find the per month payment for 20 years

363140.72 = pmt(1-(1+.0225)^-80)/.0225

363140.72 = pmt(42.4722)

pmt = $ 8,550.08

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