

UNIT
9 :
MATHEMATICS OF INVESTMENT
LESSON 2:
PRESENT VALUE
Example 1:
a) Puneet wishes to have $20 000 available in 4
years in order to purchase a new car.
If interest is 5%/a compounded
quarterly, how much should she invest today in order to amount to $20 000 in 4
years?.
Solution:
In this
example, we are given the final or future amount and we wish to find the amount
to invest today in order to accumulate to that $20 000 in 4 years. The amount we are trying to find here is
called the Present Value of $20 000 due in 4 years at 5%/a,
compounded quarterly.
The
appropriate time line is shown below.
Since there are 16 interest periods, we will put a mark every 3 months
over the 4year period.
0 1 2 3 14
15 16
20000(1.0125)^{}^{16} 20000
The
formula for the Present Value of some future amount can be determined by rearranging our formula
for compound interest and solving for P.
Example 2:
Mr. And
Mrs. Trinh would like to have $500 000 available when they retire in 20
years. How much should they invest now
if interest is 6%/a, compounded semiannually?
Solution:
The
appropriate time line is shown below.
Since there are 40 interest periods, we will put a mark every 6 months
over the 20year period.
0 1 2
3 4 .
. . 38
39 40
500000(1.03)^{40} 500000
They
should invest $153 278.42 today to achieve their goal.
Example 3:
John
would like to have $10 000 available to start up his own DOT COM business in
3 years. How much should he invest now if interest is 7.44%/a, compounded
monthly?
Solution:
He
should invest $8005.06 today to achieve his goal.