Interest on Interest: Overview, Formula, and Calculation

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Updated September 13, 2023
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Robert C. Kelly
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What Is Interest on Interest?

Interest on interest—also referred to as compound interest—is the interest earned when interest payments are reinvested. Compound interest is commonly 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.

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.

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 of Interest on Interest

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 calculated as follows:

$1,000,000 x (1+.05) ^ 5 - $1,000,000 =

$1,276,281.56-$1,000,000= $276,281.56

The compound interest is therefore $276,281.56

Do You Pay Interest on Interest?

For credit card balances, yes, you pay interest on interest. The accrued interest is added to your unpaid balance, so you are paying interest on interest. This is why it can be so hard to get out of credit card debt because even if you pay the minimum balance, the interest on the unpaid amount keeps growing. That's why it is recommended to pay your entire credit card statement balance each month.

What Is Meant by 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.

Is Interest on an Investment Considered Income?

Yes, interest on some types of investments is considered income. For example, if you have a savings account or a bond, the interest you earn on those products will be considered investment income.

The Bottom Line

Interest on interest works in favor of investors, allowing them to reap higher returns as prior interest continues to be reinvested. This is why it's important to start investing as early as possible because time is one's friend in this case. The longer the investment, the longer interest builds up and the more returns one can achieve from an investment.

Article Sources
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  1. TreasuryDirect. "I Bonds Interest Rates."

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