Compound Interest Calculator

See how a deposit and regular monthly contributions grow with compound interest: the future value, how much is interest, how much compounding adds compared with simple interest, the value in today's dollars, and how long money takes to double. Your inputs stay in your browser.

Your savings or investment

Your money

Contributions are added

Growth

The stated rate before compounding. For an account APY, choose "Annually": it gives the same result.

Compounding

Shows the result in today’s dollars.

$144,572.72 after 20 years, including $86,572.72 of interest. See full results

Example: $10,000 to start plus $200 a month at 7% compounded monthly for 20 years (illustrative; actual returns vary). Enter your numbers to update.

Your balance after 20 years

Future value
$144,572.72
APY 7.229%
Total interest
$86,572.72
On $58,000 of deposits
Extra from compounding
$39,112.72
Simple interest would give $105,460

A lump sum doubles in 9.9 years at this rate; the rule of 72 estimates 10.3 years.

Growth by year

YearDepositsInterestTotal depositedBalance
1 $2,400$801$12,400$13,201
2 $2,400$1,033$14,800$16,634
3 $2,400$1,281$17,200$20,315
4 $2,400$1,547$19,600$24,262
5 $2,400$1,832$22,000$28,495
6 $2,400$2,138$24,400$33,033
7 $2,400$2,466$26,800$37,900
8 $2,400$2,818$29,200$43,118
9 $2,400$3,196$31,600$48,714
10 $2,400$3,600$34,000$54,714
11 $2,400$4,034$36,400$61,147
12 $2,400$4,499$38,800$68,046
13 $2,400$4,998$41,200$75,444
14 $2,400$5,532$43,600$83,376
15 $2,400$6,106$46,000$91,882
16 $2,400$6,721$48,400$101,003
17 $2,400$7,380$50,800$110,783
18 $2,400$8,087$53,200$121,270
19 $2,400$8,845$55,600$132,515
20 $2,400$9,658$58,000$144,573

Compound interest formula

Compound interest is interest earned on both your deposits and the interest already added. For a single deposit P at an annual rate r compounded n times a year for t years:

A = P × (1 + r/n)n × t

At the example rate, $10,000 left alone for 20 years grows to $40,387.39. With continuous compounding the formula becomes A = P × er × t.

With a monthly contribution D, the calculator grows the balance month by month: each month the balance is multiplied by g = (1 + r/n)n/12 and the contribution is added. Over N months that sums to A = P × gN + D × (gN − 1) ÷ (g − 1). Adding $200 a month takes the example to $144,572.72; adding it at the start of each month instead gives $145,180.47, because each deposit earns one more month of interest.

How often interest compounds

More frequent compounding adds interest to the balance sooner, so it earns slightly more. The difference is small next to the rate itself. The annual percentage yield (APY) expresses any compounding as a single yearly rate (Truth in Savings definition), so to use an account's APY, enter it as the rate and choose "Annually".

$10,000 at 7% for 20 years

CompoundingAPYFinal balance
Annually 7%$38,696.84
Quarterly 7.186%$40,063.92
Monthly 7.229%$40,387.39
Daily 7.25%$40,546.56
Continuously 7.251%$40,552.00

Simple versus compound interest

With simple interest, interest is paid only on the money deposited and never on earlier interest. For the example, simple interest would give $105,460.00; compounding adds $39,112.72 more. The gap grows with time, because interest keeps earning interest.

How long to double your money: the rule of 72

Divide 72 by the annual rate in percent to estimate how many years a lump sum takes to double. At 7% that is 10.3 years; the exact figure with monthly compounding is ln 2 ÷ ln(1 + APY) = 9.9 years. The rule is a quick estimate that works best for rates between about 4% and 12%.

Inflation and real growth

Prices also rise over time, so a future balance buys less than the same amount today. Entering an inflation rate divides the result by (1 + inflation)years: at 3% inflation, the example's $144,573 is worth about $80,046 in today's dollars.

Assumptions and limits

  • The rate is fixed for the whole period. Savings rates change, and investment returns vary from year to year and can be negative; a steady rate is a simplification, not a forecast.
  • Contributions are the same every month, and nothing is withdrawn.
  • Taxes, fees and account minimums are not included.

Results are estimates for planning, not financial advice.

Methodology and testing

Automated tests compare future values for monthly, daily, quarterly and continuous compounding, start- and end-of-month contributions, simple interest and inflation with an independent closed-form calculation done to 40 significant digits. How we build and test calculators.

Sources

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    Maturity value and interest from APY or rate, compounding comparison, after-tax interest and the early-withdrawal penalty.

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    Monthly amount to reach a goal or emergency fund by a date, or time to reach it with a set deposit, with APY growth by year.

  • Loan Payoff Calculator

    Payoff date and interest saved with monthly, yearly or lump-sum extras, and the extra needed to be debt-free by a set time.

  • Dividend Calculator

    Dividend income and value over time, reinvested or taken as cash, with contributions, dividend and price growth, and tax.