Question

You have $21,371.18 in a brokerage account, and you plan to deposit an additional $5,500 at the end of every future year until your account totals $240,000. You expect to earn 8% annually on the account. How many years will it take to reach your goal? Do not round intermediate calculations. Round your answer to the nearest whole number.

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Future value of 21,371.18=21,371.18*(1.08)^n

Also:

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

=5500[(1.08)^n-1]/0.08

Hence

240,000=21,371.18*(1.08)^n+5500[(1.08)^n-1]/0.08

240,000=21,371.18*(1.08)^n+68750[(1.08)^n-1]

240,000=21,371.18*(1.08)^n+68750*(1.08)^n-68750

(240,000+68750)=(1.08)^n[21,371.18+68750]

(240,000+68750)/(21,371.18+68750)=(1.08)^n

Taking log on both sides;

log 3.42594271=n*log 1.08

n=log 3.42594271/log 1.08

=16 years(Approx).