You currently have $3,100 (Present Value) in an account that has an interest rate of 7.5% per year compounded monthly (12 times per year). You want to withdraw all your money when it reaches $6,820 (Future Value). In how many years will you be able to withdraw all your money?
We use the formula:
A=P(1+r/12)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.
6,820=3100*(1+0.075/12)^12n
(6,820/3100)=(1.00625)^12n
Taking log on both sides;
log (6,820/3100)=12n*log 1.00625
n=1/12[log (6,820/3100)/log 1.00625]
=10.55 years(Approx).
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