To calculate interest on interest, the compound interest formula determines the amount of accumulated interest on the principal amount invested or borrowed. The principal amount, the annual interest rate, and the number of compounding periods are used to calculate the compound interest on a loan or deposit.

Compound interest is the interest owed or received that grows at a faster rate than basic interest.

## How to Calculate Interest on Interest (Compound Interest)

The formula to calculate compound interest is the principal amount multiplied by 1, plus the interest rate in percentage terms, raised to the total number of compound periods. The principal amount is then subtracted from the resulting value.

Compount interest =

﻿\begin{aligned} &I = \left[P\left(1+i\right)^n\right] - P\\ &\textbf{where:}\\ &I = \text{Compound interest}\\ &P = \text{Principal}\\ &i = \text{Nominal interest rate per period}\\ &n = \text{Number of compounding periods}\\ \end{aligned}﻿

where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.

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#### Compounding: My Favorite Term

For example, assume you want to calculate the compound interest on a 1 million deposit. The principal is compounded annually at a rate of 5%. The total number of compounding periods is five years. The resulting compounded interest on the deposit is ﻿\begin{aligned} &\text{\1,000,000}*(1 + 0.05)^5 - \text{\1,000,000}\\ &=\text{\276,281.60} \end{aligned}﻿ Assume you want to calculate the compound interest on a1 million deposit. However, this particular deposit is compounded monthly. The annual interest rate is 5%, and the interest accrues at a compounding rate for five years.

To calculate the monthly interest, simply divide the annual interest rate by 12 months. The resulting monthly interest rate is 0.417%. The total number of periods is calculated by multiplying the number of years by 12 months since the interest is compounding at a monthly rate. In this case, the total number of periods is 60, or 5 years * 12 months.

The resulting interest, compounded monthly, is

﻿\begin{aligned} &\text{\1,000,000}*(1 + 0.00417)^{60} - \text{\1,000,000}\\ &=\text{\283,614.31} \end{aligned}﻿