Future value of an annuity)Upon graduating from college 30 years ago, Dr. Nick R
ID: 2809303 • Letter: F
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?
Explanation / Answer
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
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