What Is Interest-On-Interest?
Interest-on-interest, moreover referred to as ‘compound interest’, is the interest that is earned when interest expenses are reinvested. Interest-on-interest is basically used inside the context of bonds, whose coupon expenses are assumed to be re-invested and held until the bond is obtainable or matures.
Key Takeaways
- Interest-on-interest, moreover referred to as ‘compound interest’, is the interest that is earned when interest expenses are reinvested.
- It is necessarily used inside the context of bonds, whose coupon expenses are assumed to be re-invested and held until sale or maturity.
- Interest-on-interest applies to the principle amount of the bond or loan and to a few different interest that has prior to now accrued.
- Simple interest, alternatively, is only charged on the original primary amount.
Understanding Interest-On-Interest
An example of a financial protection that may pay investors interest-on-interest is the U.S. Monetary financial savings bond, which is issued by the use of a governmental body to spice up value vary from most people to fund its capital duties and other operations crucial to keep an eye on the commercial gadget.
The ones monetary financial savings bonds are zero-coupon bonds that do not pay interest until they are redeemed or mature. The interest compounds semi-annually and accrues per 30 days once a year for 30 years. Every six months, the per 30 days 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 nevertheless download the interest accrued for all the month given that Treasury only counts whole months. Any interest paid at redemption or the maturity date is then issued electronically to the bondholder’s designated bank account.
Interest-On-Interest vs. Simple Interest
Interest-on-interest differs from simple interest. While interest-on-interest applies to the principle amount of the bond or loan and to a few different interest that has prior to now accrued, simple interest is only charged on the original primary amount.
Examples of Interest-On-Interest vs. Simple Interest
Imagine 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 once as soon as a simple interest-paying Treasury Bond (T-Bond) or standard corporate bond, investors will download (5%/2) x $10,000 = 2.5% x $10,000 = $250 each price duration. In sum, they may download $500 consistent with year in interest income. Notice how the interest only applies to the par value or primary amount.
However, if the bond was once as soon as, say, a Assortment EE bond (a kind of U.S. Monetary financial savings bond), the interest calculated for a duration is added to the interest earned and accumulated from prior periods. For the reason that monetary financial savings bond does no longer pay interest until it matures, any interest earned is added once more to the principle amount of the bond, increasing its value.
With interest-on-interest, each interest price earned is added once more to the principle value for which the next interest is calculated.
The usage of our example above, the principle interest earned on the 10-year bond is $250. For the second duration, interest will then be calculated on the higher value of the bond. In this case, the interest earned for the second compounding duration is: 2.5% x ($10,000 + $250) = 2.5% x $10,250 = $256.25.
So, inside the first year an investor maintaining 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.
Calculating Interest-On-Interest
Interest-on-interest can be calculated the usage of the following elements: P [(1 + i)n – 1]
Where P = primary value
i =Â nominal annual interest rate
n = number of compounding periods
If we use this elements on the example above, we can see that an investor who holds the bond until it matures after 10 years (or 20 price 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 decide is to be had in higher than the bond that may pay simple interest. That specific bond would have earnt $5,000 instead (calculated as $500 x 10 years, or $250 x 20 compounding periods) over its lifespan.
For simplification, the interest rate used to calculate interest-on-interest can be the bond’s yield at the time the coupon price is made.
Specific Problems
Interest-on-interest is the most important consideration an investor will have to make when analyzing possible investments and forecasting an investment’s common cash return.
When calculating interest-on-interest, it’s a must to take into account that the number of compounding periods makes the most important difference. The elemental rule is that the higher the number of compounding periods, the bigger the amount of interest-on-interest.
