Simple interestis interest earned only on the original principal. It is found using
the following formula.
560 Chapter 6 Percent
Simple Interest Formula
or
where the rate ris expressed as an annual (yearly) rate and the time tis
expressed in years. This formula can be written more simply without the
multiplication raised dots as
IPrt
Interestprincipalratetime IPrt
EXAMPLE (^1) If $3,000 is invested for 1 year at a rate of 5%, how much
simple interest is earned?
StrategyWe will identify the principal, rate, and time for the investment.
WHYThen we can use the formula to find the unknown amount of simple
interest earned.
SolutionThe principal is $3,000, the interest rate is 5%, and the time is 1 year.
This is the simple interest formula.
Substitute the values for P, r , and t.
Remember to write the rate ras a decimal.
Multiply: 0.05 1 0.05.
Do the multiplication.
The simple interest earned in 1 year is $150.
The information given in this problem and the result can be presented in a
table.
I$150
I$3,0000.05
I$3,0000.05 1
IPrt
P$3,000 r5%0.05 t 1
IPrt
Self Check 1
If $4,200 is invested for 2 years at
a rate of 4%, how much simple
interest is earned?
Now TryProblem 17
3,000
0.05
150.00
Principal Rate Time Interest earned
$3,000 5% 1 year $150
If no money is withdrawn from an investment, the investor receives the principal
andthe interest at the end of the time period. Similarly, a borrower must repay the
principal andthe interest when taking out a loan. In each case, the total amountof
money involved is given by the following formula.
Finding the Total Amount
The total amount in an investment account or the total amount to be repaid on
a loan is the sum of the principal and the interest.
Total amountprincipalinterest
EXAMPLE (^2) If $800 is invested at 4.5% simple interest for 3 years, what
will be the total amount of money in the investment account at the end of the
3 years?
StrategyWe will find the simple interest earned on the investment and add it to
the principal.
Self Check 2
If $600 is invested at 2.5% simple
interest for 4 years, what will be
the total amount of money in the
investment account at the end of
the 4 years?