Compound interest calculator

Year-by-year growth

The table updates as you type. The numbers below are the example already filled in: $5,000 to start, $200 a month, 7% a year, compounded monthly, for 20 years.

Worked example

Say you open a savings account with $5,000, set up an automatic transfer of $200 a month, and earn 7% a year, compounded monthly. After 20 years you have about $124,379.03. You put in $53,000.00 ($5,000 plus 240 deposits of $200), and the other $71,379.03 is interest. Look at the table: in year 1 you earn a few hundred dollars of interest, but by year 20 the interest for that single year is bigger than the $2,400 you deposit. That's compounding doing the heavy lifting.

A simpler check: $10,000 left alone at 5% for 10 years grows to $16,470.09 with monthly compounding, $16,288.95 with yearly compounding and $16,486.65 with daily compounding.

How compound interest is calculated

For a single deposit, the calculator uses the standard formula A = P(1 + r/n)^nt, where P is the starting amount, r is the yearly rate as a decimal, n is the number of times interest compounds each year and t is the number of years. This is the same formula behind the SEC's compound interest calculator on Investor.gov.

Monthly contributions are added month by month. With monthly compounding that matches the closed formula PMT × ((1 + r/12)^12t − 1) / (r/12). With daily, quarterly or yearly compounding, each month grows by the equivalent monthly factor (1 + r/n)^n/12, so a single deposit ends the year exactly where A = P(1 + r/n)^nt says it should, and each contribution earns interest from the month it goes in. Banks credit interest on their own schedules, so expect small differences of a few dollars.

"Time to double" is ln(2) ÷ (n × ln(1 + r/n)). Results are before taxes, fees and inflation and assume the rate stays the same every year. Investments don't pay a fixed rate, so treat any long-range result as an estimate, not a promise. Investor.gov's compound interest glossary entry is a good plain-English primer.

Not sure what rate to enter for savings? The FDIC publishes the national average rates for savings accounts, money market accounts and CDs each month. Use it as a floor, then enter the rate your own bank or credit union quotes.

Put the number to work

Compounding rewards whoever starts first, so the first step is finding the monthly amount. Our guide to how much of your paycheck to save helps you pick one, and a free savings goal tracker keeps it visible. Building a cushion first? Start with an emergency fund (the free tracker helps). If you're paying high interest on a card, that interest compounds against you, so run your balances through the debt payoff calculator too.

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To project savings to a retirement age, try the retirement calculator, or the investment calculator to see the cost of fund fees.

Questions, answered

What is compound interest? Compound interest is interest you earn on your interest. Each time interest is added to your balance, the next round of interest is figured on the bigger balance, so growth speeds up over time. Simple interest, by contrast, is only ever paid on the money you put in. The longer you leave money alone, the bigger the gap between the two.

What is the compound interest formula? For a single deposit the formula is A = P(1 + r/n)^(nt), where P is the starting amount, r is the yearly rate as a decimal, n is how many times a year interest compounds and t is the number of years. With monthly contributions and monthly compounding you add PMT x ((1 + r/12)^(12t) - 1) / (r/12), where PMT is the amount you add each month.

How much is $10,000 worth after 10 years at 5%? About $16,470.09 if interest compounds monthly, $16,288.95 if it compounds once a year and $16,486.65 if it compounds daily. That is roughly $6,300 to $6,500 of interest without adding another dollar. Check it by entering $10,000, $0 a month, 5% and 10 years in the calculator above.

How much will $100 a month grow to? Saving $100 a month at a 6% yearly rate, compounded monthly, grows to about $16,387.93 after 10 years. You put in $12,000 and the other $4,387.93 is interest. Leave it for 30 years and the same $100 a month grows to roughly $100,000, which shows why time matters more than the size of each deposit.

Does compounding frequency make a big difference? Less than most people expect. On $10,000 at 5% for 10 years, daily compounding beats yearly compounding by about $198, and monthly versus daily is only about $17. Your rate, how much you add each month and how long you leave the money in matter far more than whether interest compounds daily or monthly.

What is the difference between APR and APY? APR is the plain yearly rate before compounding. APY (annual percentage yield) includes the effect of compounding within the year, so it is a little higher. A 5% rate compounded monthly is an APY of about 5.12%. Savings accounts usually quote APY. If you enter an APY in this calculator, choose Annually as the compounding so the result matches.

What is the Rule of 72? The Rule of 72 is a quick way to estimate how long money takes to double: divide 72 by the yearly rate. At 7%, 72 / 7 is about 10.3 years. The exact answer for 7% compounded monthly is about 9.9 years, which the calculator shows under "Time to double". The rule works best for rates between about 6% and 10%.

Should I add money at the start or end of the month? Adding money at the start of each month earns a little more, because every deposit gets one extra month of interest. On $100 a month at 6% for 10 years, start-of-month deposits end at about $16,469.87 versus $16,387.93 at the end of the month. Most people choose the end of the month because that matches payday.

What interest rate should I use? Use the rate you actually expect. A high-yield savings account or CD has a stated rate, so enter that. Investments such as stock index funds do not pay a fixed rate, so their future growth is a guess: try a lower and a higher rate with the "Rate range" box to see a range instead of a single number. Past returns don't guarantee future results.

Does this calculator include taxes or inflation? No. The results are before taxes, fees and inflation. Interest in a regular savings account is usually taxable each year, while retirement accounts have their own rules. To get a rough "today's dollars" figure, lower the rate by the inflation rate you expect, for example use 4% instead of 7% if you expect 3% inflation.

Is my information saved? Nothing is saved or sent. The math runs in your browser. Your numbers are kept only in the page address, so you can bookmark the page or share the exact scenario with a partner.

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