Question

TIME TO REACH A FINANCIAL GOAL You have $25,781.18 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $240,000. You expect to earn 13% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations. years

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 25781.18=25781.18*(1.13)^n

Also:

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

=5000[(1.13)^n-1]/0.13

Hence

240,000=25781.18*(1.13)^n+5000[(1.13)^n-1]/0.13

240,000=25781.18*(1.13)^n+38461.5385[(1.13)^n-1]

240,000=25781.18*(1.13)^n+38461.5385*(1.13)^n-38461.5385

(240,000+38461.5385)=(1.13)^n(25781.18+38461.5385)

(1.13)^n=(240,000+38461.5385)/(25781.18+38461.5385)

Taking log on both sides;

n*log 1.13=log 4.33452296

n=log 4.33452296/log 1.13

=12 year(Approx).