What is compound interest?
Compound interest is interest calculated on both your initial principal and the interest you have already earned. Unlike simple interest — which only grows on your original deposit — compound interest accelerates over time because your earnings begin generating their own earnings.
Albert Einstein reportedly called compound interest the eighth wonder of the world. Whether or not he said it, the math backs it up. Given enough time, even a modest sum invested at a moderate rate grows into something remarkable.
How does compound interest work?
The core idea is straightforward. When you earn interest in the first period, that interest is added to your balance. In the next period, you earn interest on the new, larger balance. This cycle repeats every compounding period — monthly, quarterly, or annually — and each cycle builds on the last.
Formula
A = P(1 + r/n)^(nt)
- A — final amount
- P — principal (your starting amount)
- r — annual interest rate (as a decimal)
- n — number of times interest compounds per year
- t — number of years
How compounding frequency affects your returns
The more frequently interest compounds, the faster your money grows. Monthly compounding produces more than annual compounding at the same rate, because you start earning interest on your interest sooner.
| Frequency | Balance after 20 years |
|---|---|
| Annually | $38,697 |
| Monthly | $40,123 |
| Daily | $40,255 |
$10,000 at 7% annual interest over 20 years.
The difference between monthly and daily compounding is small. The difference between starting now versus waiting five years is enormous.
The most important variable: time
Of all the inputs in the compound interest formula, time has the most dramatic effect. This is why financial advisors emphasize starting early above almost everything else.
An investor who puts $10,000 away at age 25 and earns 7% annually will have roughly $149,745 by age 65. An investor who waits until age 35 to invest the same amount at the same rate will have only $76,123 — about half as much — despite only a ten-year difference in start date.
Where you earn compound interest
Compound interest works in your favor in several common accounts:
- High-yield savings accounts and money market accounts compound interest daily or monthly, making them significantly more effective than traditional savings accounts for storing your emergency fund or short-term savings.
- Brokerage and retirement accounts like a 401(k) or IRA compound through investment growth and reinvested dividends. Index funds that automatically reinvest dividends are one of the simplest ways to harness long-term compounding.
- Certificates of deposit (CDs) offer fixed rates with predictable compounding, useful for money you will not need for a set period.
Compound interest working against you
The same force that builds wealth can also work in reverse. Credit card debt compounds monthly — sometimes daily — at rates of 20% or more. A $5,000 balance at 22% APR compounded monthly grows to over $6,100 in just one year if left unpaid. Paying off high-interest debt is mathematically equivalent to earning that same rate of return, risk-free.