Compound interest by formula is a quick way to calculate the interest generated on the principal, as well as the total amount available at the end of the given time period.

We saw earlier how to calculate compound interest using calculation. Now we’ll look at another method, this time using a formula given below:

**A = P (1+r) ^{n}**, where

A = Amount at the end of time period n, r = rate of interest, and n = time period.

As always, the interest is worked out according to the time period provided, e.g. annually, monthly, or daily. Also we need to convert the interest rate and the time period to the same.

For example, if the interest rate is said to compound annually, but the time period is in months, we’ll need to convert the interest rate to an equivalent monthly rate and then apply it to the formula.

Now let us look at the same two examples from the previous section.

**Example 1**: Compound interest by formula

Jessica invested $9000 for 3 years at 13% pa, interest compounded annually. Find the total interest earned by Jessica at the end of 3 years.

Here the Principal P = $9000, r = 13% pa (= 0.13), and n = 3.

Applying these values into the formula, we’ll get the Amount = $9000 (1 + 0.13)^{3}

= $9000 (1.13)^{3} = **$12986.07**.

So interest earned I = Amount A – Principal P

= $12986.07 – $9000

= **$3986.07**

**Example 2**: Compound interest by formula

What is the interest earned for 2 months on $12000 invested at 9% pa, compounded monthly.

Since N = 2 months, we need to convert the interest rate to a monthly rate as well.

Here P = $12000, R = 9% pa = = 0.75% pm (per month) = 0.0075

Now applying them all to the compound interest formula, we get

Amount A = $12000 (1 + 0.0075)^{2}

= $12000 (1.0075)^{2}

= $12180.675

or **$12180.68** (to the nearest two digits)

Interest earned I = Amount A – Principal P

= $12180.68 – $12000

= **$180.68**