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Compound Interest Calculator

See how savings grow when interest earns interest. Add regular deposits, choose how often interest is added, and watch every step with your own numbers.

Final balance

$16,470.09

After 10 years, $10,000.00 at 5% compounded monthly grows to $16,470.09. Interest earned: $6,470.09.

Interest earned
$6,470.09
Money paid in
$10,000.00
Effective yearly rate
5.1162%APY

At this rate money doubles in about 13.9 years. The rule of 72 estimates 72 ÷ 5 = 14.4.

Show me how

All steps as text

    Tip: press ← and → to move between steps, or click any step.

    Your money over time

    What the balance is made of

    Compound interest compared with simple interest

    Point at a chart, or tap it, to read the numbers. With the keyboard, select a chart and use the arrow keys. Every number is also in the table below.

    How often interest is added

    The same starting amount, rate and time with each compounding frequency.

    Interest addedFinal balanceInterest

    Year by year

    What you pay in, the interest added and the balance at the end of each year.

    Year Deposits Interest Balance

    How to use this calculator

    1. Enter the amount you start with, the yearly interest rate and how long the money stays in.
    2. Choose how often interest is added. Savings accounts often add it monthly or daily; many bonds and deposits add it yearly or twice a year.
    3. To save regularly, enter a deposit. It is made once per compounding period, at the end or at the start of each one.
    4. Under Show me how, press Play to watch the balance being worked out step by step.

    The compound interest formula

    A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}
    • A is the final balance and P the starting amount.
    • r is the yearly rate as a decimal (5% is 0.05) and n is how many times a year interest is added.
    • t is the time in years, so nt is the number of periods.

    With a deposit D at the end of every period, add the future value of the deposits, where i = r ÷ n and N = nt:

    A=P(1+i)N+D×(1+i)N−1iA = P(1+i)^N + D \times \frac{(1+i)^N - 1}{i}

    Deposits made at the start of each period earn one more period of interest, so their part is multiplied by (1 + i).

    Worked example: $10,000 at 5% compounded monthly for 10 years

    1. Rate per month: i = 0.05 ÷ 12 ≈ 0.00416667.
    2. Number of months: N = 10 × 12 = 120.
    3. Growth factor: (1 + 0.00416667)120 ≈ 1.647009.
    4. Final balance: 10,000 × 1.647009 ≈ $16,470.09.
    5. Interest: $16,470.09 − $10,000 = $6,470.09. Simple interest would have paid $5,000, so $1,470.09 of it is interest on interest.

    The interest grows every year: $511.62 in the first year and $801.62 in the tenth, on the same rate.

    Interest on interest

    Put $1,000 in an account paying 10% a year. After the first year you earn $100 and have $1,100. In the second year you earn 10% of $1,100, which is $110: the extra $10 is interest on last year's interest.

    After 10 years the balance is $2,593.74. With simple interest, which is only paid on the original $1,000, it would be $2,000. The difference grows faster every year, which is why starting early matters so much.

    Does it matter how often interest is added?

    A little. $1,000 at 10% for one year grows to:

    • $1,100.00 added yearly, $1,102.50 half-yearly and $1,103.81 quarterly,
    • $1,104.71 monthly, $1,105.06 weekly and $1,105.16 daily,
    • about $1,105.17 added continuously, using A = Pert.

    The effective yearly rate, or APY, puts these on the same footing: 10% added monthly is the same as 10.47% added once a year. Compare savings accounts by their APY.

    The rule of 72

    To estimate how long money takes to double, divide 72 by the yearly rate. At 6%, 72 ÷ 6 = 12 years; the exact answer with yearly compounding is 11.9 years. The rule works best for rates between about 4% and 12%.

    What this calculator leaves out

    It assumes the same rate for the whole time. Real savings can differ because of taxes on interest, fees, rates that change, and inflation, which lowers what the money will buy. Investment returns are not guaranteed and can be negative.

    Use the results to understand and compare, not as financial advice. See the disclaimer and how we check our math.

    Questions

    What is compound interest?

    Interest that is added to your balance, so that it earns interest itself in later periods. Simple interest is only ever paid on the original amount.

    How do I calculate compound interest?

    Divide the yearly rate by the number of periods a year, add 1, raise it to the power of the number of periods, and multiply by the starting amount: A = P(1 + r/n)nt. Press Play under Show me how to see it done with your numbers.

    What is APY?

    The annual percentage yield is the interest you earn in one year, including interest on interest, as a percentage. It is (1 + r/n)n − 1, and it is the fair way to compare accounts that add interest at different times.

    How long does it take to double my money?

    Roughly 72 divided by the yearly rate, in years. The calculator also shows the exact doubling time for your rate under the totals.

    How do I calculate it in Excel or Google Sheets?

    Use the FV function: =FV(5%/12, 120, 0, -10000) gives 16470.09 for the worked example. With a $200 monthly deposit and $10,000 at 7% for 30 years, =FV(7%/12, 360, -200, -10000) gives 325159.17. Add 1 as a fifth value for deposits at the start of each period.

    Does compound interest work against borrowers?

    Yes. On debts such as credit cards, unpaid interest is added to the balance and then charged interest too. The same formula that grows savings makes unpaid debt grow.