Compound interest is interest earned on interest. In the first year a savings account pays interest on what you deposited. In the second year it pays interest on the deposit plus the first year’s interest, and so on. Each year the base gets a little bigger, so the growth speeds up over time. The U.S. Securities and Exchange Commission’s investor education site, Investor.gov, describes it in exactly those terms, and it is the main reason that starting early matters more than almost any other savings decision.
This guide explains the formula, how compounding frequency and APY fit in, and what realistic numbers look like. You can test your own figures in the compound interest calculator.
Simple vs compound interest
With simple interest, you only ever earn interest on the original amount. $10,000 at 5% simple interest earns $500 a year, every year. After 10 years you have $15,000.
With compound interest, each year’s interest is added to the balance and earns interest itself. $10,000 at 5% compounded once a year grows to about $16,289 after 10 years. The extra $1,289 is interest on interest. Over 30 years the gap becomes dramatic: about $25,000 with simple interest against about $43,219 with annual compounding.
The simple interest calculator lets you put the two side by side.
The formula
For a single deposit, the future value is:
A = P × (1 + r/n)n×t
- P is the starting amount (the principal).
- r is the annual interest rate as a decimal (5% = 0.05).
- n is the number of times interest is compounded each year.
- t is the number of years.
Example: $5,000 at 4% compounded monthly for 8 years.
A = 5,000 × (1 + 0.04/12)96 ≈ 5,000 × 1.3764 ≈ $6,882.
Does compounding frequency matter?
It matters, but less than people expect. Here is $10,000 at 5% for 10 years at different frequencies:
- Annually: about $16,289
- Quarterly: about $16,436
- Monthly: about $16,470
- Daily: about $16,487
Moving from annual to monthly compounding adds about $181 over a decade. The interest rate and the length of time have far more effect than the frequency. A rate that is half a point higher is worth much more than daily instead of monthly compounding.
APY makes accounts comparable
Because frequency varies, U.S. banks and credit unions must show the annual percentage yield (APY) for deposit accounts under the Truth in Savings rules. APY is the total return over one year with compounding included. A 4.89% rate compounded daily works out to about a 5.01% APY.
When comparing savings accounts or CDs, compare APYs, not the headline interest rates. For loans, the comparable figure is the APR, which works differently and includes certain fees.
Regular contributions
Most people do not deposit one lump sum and walk away. They add money every month. Compounding applies to every deposit from the day it goes in, so regular saving combines two effects: the contributions themselves and growth on everything already saved.
Example: $200 a month for 30 years at a 6% annual return, compounded monthly.
- Total deposited: $72,000.
- Ending balance: about $200,900.
- Growth: roughly $128,900, much of it earned in the final decade.
Start the same plan 10 years later and run it for 20 years, and the balance is about $92,400. Ten years of extra deposits ($24,000) account for over $108,000 of the difference. That is the practical meaning of “start early.”
The savings calculator is built for this kind of monthly plan.
The Rule of 72
For a quick estimate of how long money takes to double, divide 72 by the annual rate. At 9%, money doubles in about 72 ÷ 9 = 8 years. At 6%, about 12 years. At 3%, about 24 years. The rule is an approximation that works best for rates between about 4% and 12%, but it is close enough for planning and it shows how strongly the rate drives results.
It works in reverse for costs too. At 3% inflation, prices double in roughly 24 years.
Compounding works against you on debt
The same math applies to money you owe. Credit card interest is usually calculated on a daily balance, and unpaid interest is added to the balance, which then accrues more interest. A $3,000 balance at 24% APR with only small payments can take many years to clear and cost far more than the original purchase. Paying down high-rate debt is often the best “return” available, because it is a guaranteed saving of that rate.
What compounding does not do
- It does not guarantee returns on investments. A savings account rate is fixed or known. Stock or fund returns vary from year to year, and some years are negative. Calculators use an average rate to illustrate, not to predict.
- It does not account for inflation. $200,000 in 30 years will buy less than $200,000 today. Subtract an expected inflation rate from your return for a rough “real” figure, or use the inflation calculator.
- It does not account for taxes and fees. Interest in a taxable account is generally taxed each year, and fund fees reduce your effective return. A 1% annual fee on a 6% return removes about a sixth of your growth before compounding.
Key points
- Compound interest pays interest on past interest, so growth accelerates.
- Time and rate matter far more than compounding frequency.
- Compare savings products using APY.
- Regular contributions plus time do most of the work.
- The same effect makes high-interest debt expensive.
This article is for general education. Figures are illustrations, not forecasts.
Sources
- Investor.gov (SEC): What is compound interest?
- Investor.gov (SEC): Compound interest calculator
- Consumer Financial Protection Bureau: Regulation DD (Truth in Savings)
FAQ
What does “How Does Compound Interest Work on Savings?” explain?
Compound interest is interest earned on interest. In the first year a savings account pays interest on what you deposited. In the second year it pays interest on the deposit plus the first year’s interest, and so on. Ea…
How should I use this guide with a calculator?
Read the definitions and assumptions first, then open the linked calculator with the same inputs. Treat results as estimates, not professional advice.
Is this financial or medical advice?
No. Calcenzo content is educational. Confirm important decisions with a qualified professional and official sources for your situation.