Basic Mathematics for College Students

Calculating compound interest by hand can take a long time. The compound
interest formulacan be used to find the total amount of money that an account will
contain at the end of the term quickly.

6.5 Interest 565

Compound Interest Formula

The total amount Ain an account can be found using the formula

where Pis the principal,ris the annual interest rate expressed as a decimal,tis

the length of time in years, and nis the number of compoundings in one year.

APa 1 

r

n

b

nt

A calculator is very helpful in performing the operations on the right side of the
compound interest formula.

the key is pressed instead of the key for the result to be

displayed.

Rounded to the nearest cent, the amount in the account after 3 years will be

$11,610.44.

If your calculator does not have parenthesis keys, calculate the sum within the

parentheses first. Then find the power. Finally, multiply by 9,250.

ENTER 

Using Your CALCULATOR Compound Interest

A businessperson invests $9,250 at 7.6% interest, to be compounded monthly.

To find what the investment will be worth in 3 years, we use the compound

interest formula with the following values.

P $9,250 r7.6% 0.076 t3 years n12 times a year (monthly)

This is the compound interest formula.

Substitute the values of P, r, t,and n.

In the exponent, ntmeans n t.

Evaluate the exponent: 12(3) 36.

To evaluate the expression on the right-hand side of the equation using a

calculator, we enter these numbers and press these keys.

9250 1 .076 12 36

On some calculator models, the ^ key is used in place of the yxkey. Also,

 (   ) yx  11610.43875

A9,250a 1 

0.076

12

b

36

A9,250a 1 

0.076

12

b

12 (3)

APa 1 

r

n

b

nt

EXAMPLE (^6) Compounding Daily An investor deposited $50,000 in a
long-term account at 6.8% interest, compounded daily. How much money will he
be able to withdraw in 7 years if the principal is to remain in the bank?
StrategyWe will use the compound interest formula to find the total amountin
the account after 7 years. Then we will subtract the original principal from that
result.
WHYWhen the investor withdraws money, he does not want to touch the original
$50,000 principal in the account.
Self Check 6
COMPOUNDING DAILYFind the
amount of interest $25,000 will
earn in 10 years if it is deposited
in an account at 5.99% interest,
compounded daily.
Now TryProblem 37