Basic Mathematics for College Students

562 Chapter 6 Percent

EXAMPLE (^4) Short-term Business Loans To start a business, a
couple borrowed $5,500 for 90 days to purchase equipment and supplies. If the loan
has a 14% simple interest rate, find the total amount they must repay at the end of
the 90-day period.
StrategyWe will rewrite 90 days 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 365 days in a year, we have
Simplify the fraction by
removing a common factor of 5
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.
Write $5,500 and 0.14 as fractions.
Multiply the numerators.
Multiply the denominators.
Do the division. Round to the
nearest cent.
The interest on the loan is $189.86. To find how much they must pay back, we add.
This is the total amount formula.
Substitute $5,500 for the principal and
$189.86 for the interest.
Do the addition.
The couple must pay back $5,689.86 at the end of 90 days.

$5,689.86

 $5,500 $189.86

Total amountprincipalinterest

I$189.86

I

$13,860

73

I

$5,500

1



0.14

1



18

73

I$5,5000.14

18

73

IPrt

P$5,500 r14%0.14 t

90

365



18

73

1873

90

365

90 days

90

365

year 

5

1

 18

5

1

 73

year

18

73

year

IPrt

IPrt

Self Check 4

ACCOUNTINGTo cover payroll

expenses, a small business owner

borrowed $3,200 at a simple

interest rate of 15%. Find the

total amount he must repay at

the end of 120 days.

Now TryProblem 29

770

 18

6160

7700

13,860

5,500

 0.14

22000

55000

770.00

2 Calculate compound interest.

Most savings accounts and investments pay compound interestrather than simple

interest. We have seen that simple interest is paid only on the original principal.

Compound interestis paid on the principal and previously earned interest.To illustrate

this concept, suppose that $2,000 is deposited in a savings account at a rate of 5% for

1 year. We can use the formula to calculate the interest earned at the end of

1 year.

This is the simple interest formula.

Substitute for P, r , and t.

Do the multiplication.

Interest of $100 was earned. At the end of the first year, the account contains the

interest ($100) plus the original principal ($2,000), for a balance of $2,100.

Suppose that the money remains in the savings account for another year at the

same interest rate. For the second year, interest will be paid on a principal of $2,100.

I$100

I$2,0000.05 1

IPrt

IPrt