## Compound interest calculation with formulas and how to calculate compound interest

The 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 $5,000 with annual interest of 4%.

Solution:

*A*_{0} = $5,000

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

*m* = 1

*n* = 10

*A*_{10} = $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:

*A*_{0} = $35,000

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

*m* = 12

*n* = 8

*A*_{8} = $35,000·(1+0.03/12)^{(12·8)} = $44,480.40