The Compound Interest Formula Explained

The formula looks intimidating. It is not.

Here it is, and then each piece one at a time.

The formula

A = P(1 + r/n)^(nt)

A is the final amount. P is the principal, the money you start with.

r is the annual rate written as a decimal, so 6% is 0.06. n is how many times a year interest compounds.

t is the number of years.

Take $5,000 at 6% compounded monthly for 10 years.

r/n is 0.06 / 12, which is 0.005. nt is 12 x 10, which is 120.

So A = 5,000 x (1.005)^120. That is 5,000 x 1.8194, or $9,097.

The interest earned is $4,097.

The exponent is the number of compounding periods. Each period multiplies the balance by (1 + r/n).

Raising to the power of 120 just means doing that 120 times. A calculator does it in one step.

Most people save monthly. That adds a second term.

A = P(1 + i)^N + D x ((1 + i)^N - 1) / i

Here i is the rate per period and N the number of periods. D is the deposit each period.

The second part is the future value of the deposits. It is the formula behind every savings calculator.

If compounding happens constantly the formula becomes A = Pe^(rt). The e is the constant 2.718.

In practice it gives almost the same answer as daily compounding. It matters in theory more than in your bank account.

For a quick estimate use the Rule of 72. Divide 72 by the rate to get the years to double.

At 6% that is 12 years. Our example above grew 1.8 times in 10 years, which fits.