Question

You have $21,393.30 in a brokerage account, and you plan to deposit an additional $6,000 at the end of every future year until your account totals $280,000. You expect to earn 10% 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.

Hence future value of 21,393.30=21,393.30*(1.1)^n

Also:

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

=$6000[(1.1)^n-1]/0.1

Hence

280,000=21,393.30*(1.1)^n+$6000[(1.1)^n-1]/0.1

280,000=21,393.30*(1.1)^n+$60000[(1.1)^n-1]

280,000=21,393.30*(1.1)^n+$60000*(1.1)^n-60000

(280,000+60000)=(1.1)^n[21393.30+60000]

(1.1)^n=(280,000+60000)/(21393.30+60000)

(1.1)^n=4.177248004

Taking log on both sides;

n*log 1.1=log 4.177248004

n=log 4.177248004/log 1.1

15 year(Approx).