How Compound Interest Works
Understand how interest on interest grows your savings, with a worked example, the Rule of 72, and the factors that matter most.
The short version
Compound interest means you earn interest not only on the money you originally put in, but also on the interest that money has already earned. Over short periods the difference looks small. Over decades it becomes the main reason savings grow, and the same effect works against you when you carry debt.
Simple interest vs. compound interest
With simple interest, you earn interest only on your original deposit. If you invest $10,000 at 7% simple interest for 10 years, you earn $700 each year, for a total of $7,000, and end with $17,000.
With compound interest, each year's interest is added to the balance, and next year's interest is calculated on the larger amount. The same $10,000 at 7% compounded monthly for 10 years grows to about $20,097, so you earn roughly $10,097 in interest instead of $7,000.
The compound interest formula
A = P × (1 + r/n)n×t
- A is the final amount.
- P is the starting amount (the principal).
- r is the annual interest rate as a decimal (7% = 0.07).
- n is how many times per year interest is compounded (12 for monthly, 365 for daily, 1 for yearly).
- t is the number of years.
For our example: A = 10,000 × (1 + 0.07/12)120 ≈ $20,097.
Does compounding frequency matter?
A little. Using the same $10,000 at 7% for 10 years, yearly compounding gives about $19,672, while monthly compounding gives about $20,097. More frequent compounding helps, but the difference is small compared with the effect of the interest rate and the length of time.
Adding regular contributions
Most people do not invest a single lump sum. Suppose you start with $10,000 and add $200 every month at 7% (compounded monthly) for 20 years. You would contribute $58,000 in total ($10,000 plus $200 × 240 months), and the balance would grow to roughly $144,600. About $86,600 of that is growth that you did not have to deposit yourself.
The Rule of 72
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 7%, 72 / 7 ≈ 10.3 years. At 4%, it is about 18 years. This is an approximation, but it is surprisingly accurate for typical rates.
Three factors that matter most
- Time: starting earlier is the most powerful lever. The last years of growth are far larger than the first years.
- Rate of return: higher returns grow faster, but they usually come with more risk, and returns are never guaranteed.
- Consistency: regular contributions add to the base that compounds.
Compounding works against borrowers too
Credit card balances and some loans compound as well. If you only make minimum payments on a high-rate card, interest is added to your balance and then charged interest again. This is why paying down high-interest debt is often a reliable way to improve your finances.
Frequently asked questions
Is the interest rate on my savings account compounded?
Most savings accounts compound daily or monthly. Banks often advertise the APY (annual percentage yield), which already includes the effect of compounding, so it is the best number to compare between accounts.
Do the numbers account for inflation or taxes?
No. The examples show nominal growth only. Inflation reduces what your money can buy, and taxes may apply to interest or investment gains depending on the account type and where you live.
Can I count on a 7% return?
No. The rate is an assumption used for illustration. Real investments rise and fall, and savings account rates change. Use the calculator with several different rates to see a realistic range.
Try it yourself
Use our compound interest calculator to test your own starting amount, rate, time and monthly contributions. Try changing one input at a time to see which has the biggest effect on your result.
This guide is for educational purposes only and is not financial, tax, or legal advice.