Basic Mathematics for College Students

586 Chapter 6 Percent

Interest earned in the second half of the year:

This is the simple interest formula.

Write the rate ras a decimal.

Write $10,325 and 0.065 as fractions.

Multiply the numerators.

Multiply the denominators.

Do the division. Round to the nearest cent.

The interest earned in the second half of the year is $335.56. Adding

this to the principal for the second half of the year, we get

The total amount in the account after one year is $10,660.56

$10,325$335.56$10,660.56

I$335.56

I

$671.125

2

I

$10,325

1



0.065

1



1

2

I$10,3250.065

1

2

IPrt

P$10,325 r6.5%0.065 t

1

2

Computing compound interest by hand can take

a long time. The compound interest formulacan

be used to find the amount of money that an

account will contain at the end of the term.

where Ais the amount in the account,Pis the

principal,ris the annual interest rate,nis the

number of compoundings in one year, and tis

the length of time in years.

A calculator is helpful in performing the

operations on the right side of the compound

interest formula.

APa 1 

r

n

b

nt

COMPOUNDING DAILY A mini-mall developer promises investors

in his company interest, compounded daily. If a businessman

decides to invest $80,000 with the developer, how much money will be

in his account in 8 years?

Compounding dailymeans the compounding will be done 365 times a

year.

This is the compound interest formula.

Substitute for P, r, n, and t.

Evaluate the exponent: 365  8 2,920.

Use a calculator. Round to the nearest cent.

There will be $103,753.21 in the account in 8 years.

A103,753.21

A80,000a 1 

0.0325

365

b

2,920

A80,000a 1 

0.03 25

365

b

365 (8)

APa 1 

r

n

b

nt

P$80,000 r 3

1

4

%0.0325 t 8 n 365

3 14 %