Question

You have $22,566.87 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $280,000. You expect to earn 11% annually on the account. How many years will it take to reach your goal? 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.

Hence A for $22,566.87=22,566.87*(1.11)^n

Also:

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

=$5000[(1.11)^n-1]/0.11

Hence

280000=22,566.87*(1.11)^n+$5000[(1.11)^n-1]/0.11

280000=22,566.87*(1.11)^n+$45,454.545[(1.11)^n-1]

280000=22,566.87*(1.11)^n+$45,454.545(1.11)^n-45,454.545

(280,000+45,454.545)=(1.11)^n[22,566.87+45,454.545]

(1.11)^n=(280,000+45,454.545)/[22,566.87+45,454.545]

(1.11)^n=4.784589431

Taking log on both sides;

n*log 1.11=log 4.784589431

n=log 4.784589431/log 1.11

=15 years.

answered by: anonymous