Compound interest explained: formula, Rule of 72 and what monthly deposits add
Compound interest means you earn interest on your interest. The longer money stays invested, the faster the balance grows.
The formula
A = P × (1 + r ÷ n)n × t, where P is the starting amount, r is the annual rate, n is how many times a year interest is added and t is the number of years. With regular deposits, each deposit also grows from the day it is added.
Example: $10,000 at 7%, compounded monthly
| Years | No deposits | + $200 a month |
|---|---|---|
| 10 | $20,097 | $54,714 |
| 20 | $40,387 | $144,573 |
| 30 | $81,165 | $325,159 |
After 20 years with monthly deposits you have put in $58,000 ($10,000 plus $48,000), so $86,573 of the final balance is interest. In the no-deposit case the money roughly doubles every 10 years.
Skip the maths, try your own numbersCompound Interest CalculatorFree, instant, no sign-up →The Rule of 72
Divide 72 by the annual rate to estimate how many years it takes to double. At 7% that is 72 ÷ 7 ≈ 10.3 years (the exact figure is about 10.2). At 4% it is about 18 years.
Three levers you control
- Time: starting 10 years earlier matters more than a higher rate.
- Deposits: regular contributions do most of the work in the early years.
- Fees: a 1% yearly fee reduces your effective rate by about a seventh at 7%.
These figures assume a constant 7% return. Real returns vary year to year and are never guaranteed, so use the calculator below for planning scenarios, not predictions.
Simple vs compound interest
With simple interest you earn interest only on the original amount. With compound interest you earn interest on the original amount and on past interest. $10,000 at 7% simple interest for 10 years earns $7,000 for a total of $17,000. With monthly compounding it grows to $20,097. The gap widens each year.
Does compounding frequency matter?
| Compounded | $10,000 at 7% after 10 years |
|---|---|
| Annually | $19,672 |
| Quarterly | $20,016 |
| Monthly | $20,097 |
| Daily | $20,136 |
Frequency matters a little, but rate and time matter far more. A 7% rate compounded monthly has an effective annual yield of about 7.23%.
The power of starting early
Saving $200 a month at 7% from age 25 to 65 (40 years) grows to roughly $525,000. Starting at 35 (30 years) gives about $244,000. The extra ten years contribute only $24,000 of deposits but more than double the result. Time in the market lets early deposits compound for longer.
What fees do to your return
On $10,000 plus $200 a month for 30 years, a 7% return gives about $325,000. If fees reduce your net return to 6%, the result is about $261,000, roughly $64,000 less. A 1% fee sounds small but takes a large share of long-term growth. Compare fund expense ratios and platform fees when you invest.
Inflation: nominal vs real returns
The figures here are nominal, meaning they are not adjusted for rising prices. If inflation averages 3%, a 7% return is about 4% in real terms. When you plan for a goal such as retirement or a home, think in today's money and use a lower real return in the calculator.
Compound interest works against you on debt
Credit cards and some loans compound against you. A balance carried at 22% APR roughly doubles in under 4 years if you add nothing and pay nothing, by the Rule of 72. Paying down high-interest debt gives a guaranteed return equal to the interest rate.
The Rule of 72 and its limits
Divide 72 by the annual rate to estimate the years to double: 72 ÷ 10 = 7.2 years, 72 ÷ 7 ≈ 10.3 years, 72 ÷ 4 = 18 years. It works well for rates between about 6% and 10% and is an approximation, not an exact figure.
How to use the calculator
Enter your starting balance, monthly deposit, expected annual rate, compounding frequency and number of years. Try a conservative rate and an optimistic one to see a range. No investment return is guaranteed, and markets can fall as well as rise.
Troubleshooting: common problems and fixes
- My bank shows a different balance. The bank may compound daily, charge fees or pay a variable rate. Match the rate and frequency in the calculator.
- Results look too good to be true. A constant 7% is an assumption. Use a lower rate to see a cautious case.
- I am not sure what rate to use. Use the rate on your account for savings, or a long-term assumption for investments. Do not treat it as a promise.
- I want to include inflation. Use a real return, which is your expected return minus inflation.
- Tax is not included. Interest and gains may be taxed. Rules depend on your country and account type.
How accurate is this?
The calculator applies the standard compound interest formula with regular monthly deposits. It assumes a constant rate, which real investments do not provide, and it ignores tax, fees and inflation unless you adjust the rate. Use it for planning scenarios and not as a forecast. Nothing is sent to a server.
More free Zyphub tools you may need
- Compound Interest Calculator: See how savings grow over time.
- Mortgage & Loan Calculator: Monthly payment and total interest.
- Percentage Calculator: % of, % change, increase and decrease.
Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt), where P is the principal, r the annual rate, n the compounding periods per year and t the years.
How much will $200 a month grow to in 30 years at 7%?
With a $10,000 starting balance, about $325,000. Without the starting balance, deposits alone grow to roughly $244,000.
What is the Rule of 72?
A shortcut: divide 72 by the annual return to estimate how many years it takes money to double. At 7% that is about 10 years.
Does compounding monthly beat compounding annually?
Yes, slightly, because interest is added to the balance more often. The difference is small compared with the effect of rate and time.
Are the results guaranteed?
No. The calculator assumes a constant rate. Real investment returns vary and are not guaranteed.
How is compound interest different from simple interest?
Simple interest is calculated only on the original amount. Compound interest includes previously earned interest, so growth accelerates.
How long does it take to double money at 8%?
About 9 years by the Rule of 72 (72 ÷ 8).