What it means
With simple interest, you earn interest only on the original amount you invested or lent. With compound interest, each period's interest is added to the balance, and the next period's interest is calculated on the larger total.
The additional amount earned on the previously earned interest is the interest on interest. In the early years the effect is small, because there is little accumulated interest to earn on.
As time passes, it grows steadily and eventually becomes a large share of the total return. This is why long-term savers and investors are encouraged to start early and leave the money alone.
It matters for bonds in a specific way. A bond pays regular coupons, and the total return depends on what the investor can earn by reinvesting those coupons.
For long-dated bonds, interest on interest can make up a large part of the final return, so the reinvestment rate is critical. The effect also works against borrowers.
On a loan or credit card where unpaid interest is added to the balance, the borrower ends up paying interest on interest. This is why high-rate debt can grow so quickly when payments are missed.
Frequency makes a difference. The more often interest is added, whether monthly, daily or annually, the more interest on interest is generated for the same stated annual rate.
That is why lenders and savings providers quote an effective annual rate to allow fair comparison. Finance teams use the concept when valuing investments, planning long-term savings such as pension contributions and comparing loan offers.
Ignoring it can lead to a large underestimate of how much an investment will grow or how much a debt will cost.
In practice
Real-world examples.
Example
A young employee pays into a retirement fund each month and leaves the earnings invested. After thirty years, a large part of the balance comes from interest earned on earlier interest. The employee checks the statement each year and sees that the growth is faster in the later years than in the early ones.
Example
A bond investor receives coupons of $4,000 a year and reinvests each one at 4%. When the bond matures, the extra income from reinvested coupons forms a meaningful part of the total return.
Example
A small business owner misses payments on a high-rate credit line. Unpaid interest is added to the balance each month, so the next month's interest is charged on a larger amount, and the debt grows faster than expected.
Formula
Calculation
Future value = Principal x (1 + rate) ^ years
Interest on interest = Compound interest - Simple interest
An investor puts $10,000 into an account paying 5% a year, compounded annually, for 3 years. Year 1: 10,000 x 1.05 = $10,500. Year 2: 10,500 x 1.05 = $11,025. Year 3: 11,025 x 1.05 = $11,576.25.
Total compound interest = 11,576.25 - 10,000 = $1,576.25. Simple interest would be 10,000 x 0.05 x 3 = $1,500. Interest on interest = 1,576.25 - 1,500 = $76.25.Case study
Seen in the real world.
Fernbank Retirement Services is an illustrative, fictional firm that helps employees plan their savings. A sales manager aged 25 asked whether it mattered if he waited five years to begin saving $200 a month.
The adviser used a simple model at a 6% annual return. Starting at 25 for 40 years meant contributions of 200 x 12 x 40 = $96,000, whereas starting at 30 for 35 years meant 200 x 12 x 35 = $84,000, a difference of only $12,000 in contributions.
The model showed that the final balance was much lower for the later starter, because the early contributions had more time to earn interest on interest. In this illustrative story, the manager decided to begin immediately and to increase his payments each year. The adviser also stressed that the same logic applied to the sales manager's debts, so he paid off a credit card balance before starting the larger monthly savings plan. He had not appreciated that unpaid interest would otherwise keep joining the balance and earning more interest for the lender. The adviser also reminds clients that the stated rate and the effective rate can differ, so the compounding frequency should be compared before choosing a product.
Watch out
Common mistakes.
- Confusing simple and compound interest, which leads to a large underestimate of long-term growth.
- Forgetting that debt works the same way, so unpaid interest can quickly snowball.
- Assuming that a small difference in rate or frequency is unimportant, when over long periods it can change the outcome substantially.
Questions
People also ask.
Is interest on interest the same as compound interest?
It is the part of compound interest that comes from earlier interest, and the total compound interest equals the simple interest plus the interest on interest.
Why do bonds depend on reinvestment?
Coupons are paid out as cash, and the return you earn depends on what rate you can earn when you reinvest them.
How can I reduce interest on interest on my debts?
Pay at least the interest due each period and clear high-rate balances first, so that unpaid interest does not join the balance.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%