Interest-On-Interest Explained: Key Concepts and Calculation

What Is Interest-on-Interest?

Interest-on-interest, commonly known as compound interest, refers to the process where interest earned is reinvested to earn more interest. This financial mechanism is predominantly applied to bonds, where interest payments or 'coupons' are assumed to be reinvested until the bond matures or is sold.

Understanding interest-on-interest is crucial because it directly influences the growth potential of your investments over time through the accumulation of earned interest on top of both principal and previously accrued interest. We'll tell you how to calculate interest-on-interest and show you examples comparing it to simple interest to help you maximize your investment returns.

How Interest-on-Interest Works

An example of a financial security that pays investors interest-on-interest is the U.S. Savings bond, which is issued by a governmental body to raise funds from the public to fund its capital projects and other operations necessary to manage the economy.

These savings bonds are zero-coupon bonds that do not pay interest until they are redeemed or mature. The interest compounds semi-annually and accrues monthly every year for 30 years. Every six months, the monthly interest calculation is adjusted to include the accrued interest from the previous six months.

An investor who purchases the bond at the end of the month will still receive the interest accrued for the entire month since the Treasury only counts full months. Any interest paid at redemption or the maturity date is then issued electronically to the bondholder’s designated bank account.

Comparing Interest-on-Interest and Simple Interest

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

Examples of Interest-on-Interest vs. Simple Interest

Consider a bond issued with a $10,000 par value and 10 years to maturity. The interest rate on the bond is 5% and compounds semi-annually. If this bond was a simple interest-paying Treasury Bond (T-Bond) or conventional corporate bond, investors will receive (5%/2) x $10,000 = 2.5% x $10,000 = $250 each payment period. In sum, they would receive $500 per year in interest income. Notice how the interest only applies to the par value or principal amount.

On the other hand, if the bond was, say, a Series EE bond (a type of U.S. Savings bond), the interest calculated for a period is added to the interest earned and accumulated from prior periods. Since the savings bond does not pay interest until it matures, any interest earned is added back to the principal amount of the bond, increasing its value.

Using our example above, the first interest earned on the 10-year bond is $250. For the second period, interest will then be calculated on the increased value of the bond. In this case, the interest earned for the second compounding period is: 2.5% x ($10,000 + $250) = 2.5% x $10,250 = $256.25.

So, in the first year an investor holding this bond will earn $250 + $256.25 = $506.25. The third interest can be calculated as 2.5% x ($10,250 + 256.25) = $262.66, and so on.

How to Calculate Interest-on-Interest

Interest-on-interest can be calculated using the following formula: P [(1 + i)n – 1]

Where P = principal value

i = nominal annual interest rate

n = number of compounding periods

If we use this formula on the example above, we can see that an investor who holds the bond until it matures after 10 years (or 20 payment periods) will earn:

Interest-on-interest = $10,000 x (1.025²⁰ – 1)

= $10,000 x (1.6386 – 1)

= $10,000 x 0.638616

= $6,386.16

This figure comes in higher than the bond that pays simple interest. That particular bond would have earnt $5,000 instead (calculated as $500 x 10 years, or $250 x 20 compounding periods) over its lifespan.

Important Considerations for Interest-on-Interest

Interest-on-interest is an important consideration an investor must make when analyzing potential investments and forecasting an investment's total cash return.

When calculating interest-on-interest, it's important to remember that the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of interest-on-interest.