# Compound Interest Formula

Compound interest calculation formula with examples.

## Compound interest calculation formula

### Future value calculation

The future amount after n years A_{n} is equal to the initial amount A_{0}
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:

A_{n} is the amount after n years (future value).

A_{0} 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 $3,000 with annual interest of 4%.

Solution:

*A*_{0} = $3,000

*r* = 4% = 4/100 = 0.04

*m* = 1

*n* = 10

*A*_{10} = $3,000·(1+0.04/1)^{(1·10)} = $4,440.73

#### Example #2:

Calculate the future value after 8 years present value of $40,000 with annual interest of 3% compounded monthly.

Solution:

*A*_{0} = $40,000

*r* = 3% = 3/100 = 0.03

*m* = 12

*n* = 8

*A*_{8} = $40,000·(1+0.03/12)^{(12·8)} = $50,834.74

#### Example #3:

Calculate the future value after 8 years present value of $50,000 with annual interest of 4% compounded monthly.

Solution:

*A*_{0} = $50,000

*r* = 4% = 4/100 = 0.04

*m* = 12

*n* = 8

*A*_{8} = $50,000·(1+0.04/12)^{(12·8)} = $68,819.76

#### Example #4:

Calculate the future value after 8 years present value of $70,000 with annual interest of 5% compounded monthly.

Solution:

*A*_{0} = $70,000

*r* = 5% = 5/100 = 0.05

*m* = 12

*n* = 8

*A*_{8} = $70,000·(1+0.05/12)^{(12·8)} = $104,340.98

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## See also