# Compound interest formula

Compound interest calculation formula with examples.

## Compound interest calculation formula

### Future value calculation

The future amount after n years An is equal to the initial amount A0 times one plus the annual interest rate r divided by the number of compounding periods in a year m raised to the power of m times n: An is the amount after n years (future value).

A0 is the initial amount (present value).

r is the nominal annual interest rate.

m is the number of compounding periods in one year.

n is the number of years.

#### Example #1:

Calculate the future value after 10 years present value of \$5,000 with annual interest of 4%.

Solution:

A0 = \$5,000

r = 4% = 4/100 = 0.04

m = 1

n = 10

A10 = \$5,000·(1+0.04/1)(1·10) = \$7,401.22

#### Example #2:

Calculate the future value after 8 years present value of \$35,000 with annual interest of 3% compounded monthly.

Solution:

A0 = \$35,000

r = 3% = 3/100 = 0.03

m = 12

n = 8

A8 = \$35,000·(1+0.03/12)(12·8) = \$44,480.40

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