Question

1) You expect to receive $7,000 at graduation in two years. You plan on investing it at 10 percent until you have $103,000. How long will you wait from now

2)Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2016, a sculpture was sold at auction for a price of $10,316,500. Unfortunately for the previous owner, he had purchased it in 2012 at a price of $12,379,500. What was his annual rate of return on this sculpture?

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.

1.

103,000=7000*(1.1)^n

(103,000/7000)=(1.1)^n

Taking log on both sides;

log (103,000/7000)=n*log 1.1

n=log (103,000/7000)/log 1.1

=28.21 years(Approx)

Hence time to wait from now=28.21+2

=30.21 years(Approx)

2.

10,316,500=12,379,500*(1+r/100)^4

(10,316,500/12,379,500)^(1/4)=(1+r/100)

(1+r/100)=0.955448581

r=0.955448581-1

=-4.46%(Approx)(Negative)