Question

Upon graduating from college 35 years​ ago, Dr. Nick Riviera was already planning for his retirement. Since​ then, he has made deposits into a retirement fund on a semiannually basis in the amount of ​$600. Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned 11 percent compounded semiannually. Use five decimal places for the periodic interest rate in your calculations.
a. How much has Nick accumulated in his retirement​ account?
b. In addition to​ this, 15 years ago Nick received an inheritance check for ​$20,000 from his beloved uncle. He decided to deposit the entire amount into his retirement fund. What is his current balance in the​ fund?

Answer 1

a) Since it is an annuity, we use the Future value of Annuity formula

Here P = 600, n = 35 x 2 = 70, r = 11%/2 = 5.5%

Hence FV = 600 x [(1.055)⁷⁰ -1)/0.055] = 451,962.72

b) We use the Compounding Formula for the 20,000 deposited for a period of N' = 15 x 2 = 30
Rate per period is 5.5%

Hence FV = PV.(1 + r)^N' = 20,000 x (1.055)³⁰ = 99,679.03

Therefore Total Fund Balance = 99,679.03 + 451,962.72 = 551,641.75