# Compound Interest Formula

Compound interest is the interest in which you earn interest on your money invested as well as the interest earned on initial money.

Let's suppose you have deposited 1000\$ with a 5% monthly initial interest rate. After a month, you would have earned 5% on 1000\$ (i.e 1000\$ X 5% = 50\$). But in the second month, you just not earn 5% on your 1000\$ but also on 50\$ earned in the first month via interest of 5%. This addition of interest is referred to as compound interest.

This page offers all the details, formulas & calculations of compound interest with examples.

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

How long does it take compound interest to double?

The standard expresses that to find the quantity of years expected to twofold your cash at a given loan fee, you simply partition the financing cost into 72. For instance, if you need to know what amount of time it will require to twofold your cash at eight percent premium, partition 8 into 72 and get 9 years.