Basic Mathematics for College Students

6.5 Interest 561

WHYAt the end of 3 years, the total amount of money in the account is the sum Now TryProblem 21
of the principal and the interest earned.

SolutionThe principal is $800, the interest rate is 4.5%, and the time is 3 years. To
find the interest the investment earns, we use multiplication.

This is the simple interest formula.

Substitute the values for P, r , and t.

Remember to write the rate ras a decimal.

Multiply: $800 0.045 $36.

Do the multiplication.

The simple interest earned in 3 years is $108. To find the total amount of money in
the account, we add.

This is the total amount formula.

Substitute $800 for the principal and

$108 for the interest.

Do the addition.

At the end of 3 years, the total amount of money in the account will be $908.

$908

 $800  $108

Total amountprincipalinterest

I$108

I$36 3

I$8000.045 3

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P$800 r4.5%0.045 t 3

3

1

6

 3

108

0.04

4

5

 800

36.000

Caution! When we use the formula ,the time must be expressed in

years. If the time is given in days or months, we rewrite it as a fractional part

of a year. For example, a 30-day investment lasts 36530 of a year, since there are

IPrt

365 days in a year. For a 6-month loan, we express the time as or of a year,

since there are 12 months in a year.

126 12

EXAMPLE (^3) Education Costs A student borrowed $920 at 3% for
9 months to pay some college tuition expenses. Find the simple interest that must
be paid on the loan.
StrategyWe will rewrite 9 months as a fractional part of a year, and then we will
use the formula to find the unknown amount of simple interest to be paid
on the loan.
WHYTo use the formula , the time must be expressed in years, or as a
fractional part of a year.
SolutionSince there are 12 months in a year, we have
Simplify the fraction by removing
a common factor of 3 from the
numerator and denominator.
The time of the loan is year. To find the amount of interest, we multiply.
This is the simple interest formula.
Substitute the values for P, r , and t.
Remember to write the rate ras a decimal.
Write $920 and 0.03 as fractions.
Multiply the numerators.
Multiply the denominators.
Do the division.
The simple interest to be paid on the loan is $20.70.

I$20.70

I

$82.80

4

I

$920

1



0.03

1



3

4

I$9200.03

3

4

IPrt

P$920 r3%0.03 t

3

4

34

9

12

9 months

9

12

year 

3

1

 3

3

1

 4

year

3

4

year

IPrt

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Self Check 3

SHORT-TERM LOANSFind the

simple interest on a loan of $810

at 9% for 8 months.

Now TryProblem 25

2

2

7

1

.60

 3

82.80

920

 0.03

27.60

20.70

(^4)  82.80
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02
 0
28
 28
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