Question

7. How many years will it take for $136,000 to grow to be $468,000 if it is invested in an account with an annual interest rate of 8%?

8. At what annual interest rate must $10,000 be invested so that it will grow to be $475,000 in 20 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.

a.

468,000=136,000*(1.08)^n

(468,000/136,000)=(1.08)^n

Taking log on both sides;

log (468,000/136,000)=n*log 1.08

n=log (468,000/136,000)/log 1.08

=16.06 years(Approx).

b.

475,000=10,000*(1+r/100)^20

(475,000/10,000)^(1/20)=(1+r/100)

(1+r/100)=1.2129

r=1.2129-1

=21.29%(Approx).