# How to Calculate Interest on Interest

Interest on interest—also referred to as compound interest—is the interest earned when interest payments are reinvested. Compound interest is used in the context of bonds. Coupon payments from bonds are assumed to be reinvested at some interest rate and held until the bond is sold or matures.

Compound interest refers to the interest owed or received on an investment, and it grows at a faster rate than simple interest.

### Key Takeaways:

• Interest on interest is the interest earned when interest payments are reinvested, particularly in the context of bonds.
• This is also known as compound interest, or compounding.
• Compound interest grows at a faster rate than basic interest, and it will be fastest when compounding periods are most frequent.
• Simple interest, in contrast, only credits the original amount of principal.
• Coupon payments from bonds can be reinvested at some compound interest rate and held until the bond is sold or matures. Dividends can also be reinvested to compound stock returns.
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## How Interest on Interest Works

Interest on interest works, as the term implies, by paying interest on past interest payments received as well as on the initial amount of principal invested or saved.

For example, U.S. Savings bonds are financial securities that pay interest on interest to investors with interest that compounds semi-annually and accrues monthly every year for 30 years. Most savings accounts at banks also pay interest on interest, with payments compounded on a monthly basis.

Interest on interest differs from simple interest. Simple interest is only charged on the original principal amount while interest on interest applies to the principal amount of the bond or loan and to any other interest that has previously accrued.

## How to Calculate Interest on Interest

When calculating 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.

The formula to calculate compound interest is to add 1 to the interest rate in decimal form, raise this sum to the total number of compound periods, and multiply this solution by the principal amount. The original principal amount is subtracted from the resulting value.

Compound interest:

The "rule of 72" estimates the number of years it will take for the value of an investment or savings to double when there is interest on interest. Divide the number 72 by the interest rate to get the approximate number of years.

## Example

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, representing five one-year periods.

The resulting compounded interest on the deposit is as follows:

## What Is Interest on Interest?

Interest on interest refers to an investment or deposit whereby interest that has been credited in the past is also used for calculating future interest payments. Because interest on interest compounds over time, it can grow exponentially as time passes.

## What Is Another Name for Interest on Interest?

Interest on interest is also known as compound interest, or simply as compounding.

## What Is Interest?

Interest refers to payments made on investments, loans, or deposits. In particular, interest is payment received due to the opportunity cost of lending, depositing, or investing money to somebody else rather than utilizing yourself over some period of time. The greater the time period or the greater the perceived risk involved with handing over your money, the higher the rate of interest required. Interest may, therefore, be thought of as the "cost of money" or the cost of the "time value of money."

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1. U.S. Securities and Exchange Commission. "What Is Compound Interest?"

2. Treasury Direct. "Series I Savings Bonds Rates & Terms: Calculating Interest Rates."

3. Consumer Financial Protection Bureau. "What's the Difference Between a Simple Interest Rate and Precomputed Interest in an Auto Loan Contract?"

4. U.S. Securities and Exchange Commission. "Compound Interest Calculator."