Sam refuses to retire until his retirement account has a bal

Sam refuses to retire until his retirement account has a balance of at least $1 million.  The account currently has a balance of $500,000, and earns a rate of 9%, compounded monthly. If Sam does not plan to make any more deposits into hisaccount, how long will he have to wait until he retires?

A. 7.8 years

B. 15.2 years

C. 9.4 years

D. 12.1 years

Solution

We use the formula:
A=P(1+r/1200)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.

1,000,000=500,000(1+0.09/12)^12n

(1,000,000/500,000)=(1.0075)^12n

2=(1.0075)^12n

Taking log on both sides;

log 2=12n*log(1.0075)

n=1/12[log 2/log(1.0075)]

which is equal to

=7.8 years(Approx).