Calculating Present values:
For each of the following, compute the present value:
Present Value
Years
Interest Rate
Future Value
$10,823.02
12
4%
17,328
$29,411.69
4
9%
41,517
$128,928.43
16
12%
790,382
$72,388.42
21
11%
647,816
PV=FV/(1+r)
t
=17,328 /(1+0.04)^12=$10,823.02
#9,
Calculating the number of periods.
You’re trying to save to buy a new $160,000 Ferrari. You have $25,000 today that can be invested at your
bank. The bank pays 4.7 percent annual interest on its account. How long will it be before you have
enough to buy the car
Present value=FV/ (1+r) ^t
Solving for t:
t=In( FV/PV)/In(1+r)
t=In(160,000/$25,000)/In 1.047=58.93 years
#14,
Calculating Rates of return
Although appealing to more refined tastes, art as a collectible has not always performed so profitably.
During 2003, Sotheby’s sold the edges degas sculpture petite
denseuse de quatorze ans
at auction for a
price of $10,377,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of
$12,377,500. What was his annual rate of return on this sculpture?
FV=PV (1+r) ^t