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

Explanation:

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 future value of $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

280,000=22,566.87*(1.11)^n+$5000[(1.11)^n-1]/0.11

280,000=22,566.87*(1.11)^n+$45,454.55[(1.11)^n-1]

280,000=22,566.87*(1.11)^n+$45,454.55*(1.11)^n-45,454.55

(280,000+45,454.55)=(1.11)^n[22566.87+45,454.55]

(1.11)^n=(280,000+45,454.55)/[22566.87+45,454.55]

(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(Approx).