Interest-On-Interest
What Is Interest-On-Interest?
Interest-on-interest, additionally alluded to as 'accumulate interest', is the interest that is earned when interest payments are reinvested. Interest-on-interest is fundamentally utilized in the context of bonds, whose coupon payments are assumed to be re-invested and held until the bond is sold or matures.
Understanding Interest-On-Interest
An illustration 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 important to deal with the economy.
These savings bonds are zero-coupon bonds that don't pay interest until they are redeemed or mature. The interest compounds semi-annually and builds monthly consistently for quite a long time. At regular intervals, the monthly interest calculation is adjusted to incorporate the accrued interest from the previous six months.
An investor who purchases the bond at the month's end 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.
Interest-On-Interest versus Simple Interest
Interest-on-interest varies from simple interest. While interest-on-interest applies to the principal amount of the bond or loan and to whatever other interest that has previously accrued, simple interest is only charged on the original principal amount.
Instances of Interest-On-Interest versus 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 accumulates semi-annually. Assuming 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 every payment period. In sum, they would receive $500 each year in interest income. Notice how the interest only applies to the par value or principal amount.
On the other hand, on the off chance that 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 doesn't pay interest until it matures, any interest earned is added back to the principal amount of the bond, expanding its value.
With interest-on-interest, each interest payment earned is added back to the principal value for which the next interest is calculated.
Utilizing our model over, 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.
Thus, 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, etc.
Calculating Interest-On-Interest
Interest-on-interest can be calculated utilizing the accompanying formula: P [(1 + i)n - 1]
Where P = principal value
I = nominal annual interest rate
n = number of compounding periods
Assuming we utilize this formula on the model 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 life expectancy.
For simplification, the interest rate used to calculate interest-on-interest can be the bond's yield at the time the coupon payment is made.
Special Considerations
Interest-on-interest is an important consideration an investor must make while examining potential investments and forecasting an investment's total cash return.
While calculating interest-on-interest, it's memorable's important that the number of compounding periods has a significant effect. The fundamental rule is that the higher the number of compounding periods, the greater the amount of interest-on-interest.
Highlights
- Simple interest, on the other hand, is only charged on the original principal amount.
- Interest-on-interest, additionally alluded to as 'accumulate interest', is the interest that is earned when interest payments are reinvested.
- Interest-on-interest applies to the principal amount of the bond or loan and to whatever other interest that has previously accrued.
- It is basically utilized in the context of bonds, whose coupon payments are assumed to be re-invested and held until sale or maturity.
