Answer:
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).
