Simple Interest

1
Simple Interest

• Introducing the Mathematics of Finance

2
Notes about Simple Interest
For a short-term loan (perhaps a loan to a
friend), simple interest may be used. For
simple interest, the interest is determined just
once, at the end of the loan.
Later, well study compound interest where the
interest is applied at regular periods.
3
3 months of interest
Suppose you make a loan of 2000 for which you
charge 8 annually in simple interest. If the
loan is repaid at the end of 3 months, how much
interest should you be paid?
4
3 months of interest
If the rate is 8, the interest is 8 of 2000
per year. A total of (2000)(0.08) 160
interest for one year.
But since the loan was for just 3 months or 3/12
of a year, you are paid this fraction of the
yearly interest. The interest paid is
(2000)(0.08)(3/12) 40.00
5
Simple Interest Formula
For a loan of P dollars at a simple interest rate
r, the interest I is given by where t is the
duration (in years) of the loan.
6
18 month investment
Suppose a short-term investment offers 10 simple
interest. If you invest 4000 in such an
account, what is the value of the investment 18
months later?
The interest earned is Prt
(4000)(0.10)(18/12) 600.
And so, the total value of the investment is A
P Prt 4000 600 4600.
7
Investing today
Again, suppose a short-term investment offers 10
simple interest. How much should be invested in
the account today in order for the account to
have a future value of 7500 at the end of 18
months?
Here, were asked to find the initial amount P.
8
Present Value
To have a future value of 7500 at the end of 18
months,
Note the parentheses!
9
Now and Later
Initial amount or principal, P
Accumulated total value, A
present value
future value
6521.74
7500.
0 years
after 1.5 years
10
Examples
Suppose a short-term investment offers 6.5
simple interest.

• If you invest 1200 in such an account, what
  is the value of the investment 14 months later?
• How much needs to be invested today in order
  for the account to have a value of 1500 at the
  end of 14 months?

11
Find the simple interest rate
You borrow 1400 and agree to pay simple
interest. At the end of 18 months, you write a
check for 1589 to payoff the loan. What was the
rate of simple interest?
Set up the equation A P Prt ,then solve for
r.
12
Time to double?
How long does it take for an investment to double
in value if it earns 15 simple interest?
Since the value has doubled, we know A 2P.