Question

Future value of an​ annuity)  Upon graduating from college

30

years​ ago, Dr. Nick Riviera was already planning for his retirement. Since​ then, he has made deposits into a retirement fund on a

monthly

basis in the amount of

​$100.

Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned

12

percent compounded

monthly.

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

​$25,000

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.

Number of monthly deposits in the retirement fund = 30 years * 12 = 360

Monthly interest rate = 12%/12 = 1% = 0.01

Amount of monthly deposits = $100

Future value of annuity = Annuity amount*{(1+r)ⁿ-1}/r

Amount accumulated in the retirement account = $100*(1.01³⁶⁰-1)/0.01 = $349,496.41

b.

Amount of inheritance check = $25,000

Number of months of compounding = 15 years * 12 = 180

Value of inheritance check deposited = $25,000*1.01¹⁸⁰ = $149,895.05

Current balance in the retirement fund = $349,496.41 + $149,895.05 = $499,391.46