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Compound interest calculator

Compound interest pays a return on both the original principal and on all previously accrued interest. The balance after t years is A = P(1 + r/n)^(nt), extended by PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)] when contributions are added each period. $5,000 growing at 7% with $300 added monthly reaches $176,472 after 20 years.

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years
Calculated in your browser — nothing is uploaded.

Result

Balance after 20 years

$176,472

A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]

Total contributed
$77,000
Interest earned
$99,472
Interest share of balance
56.4%
Effective annual rate (APY)
7.229%

$5,000 invested at 7.00% compounded 12 times a year, plus $300 added each period, grows to $176,472 after 20 years. Of that total, $99,472 is compound interest.

How to use the compound interest calculator

  1. 01

    Enter the starting amount

    Type the lump sum you begin with. Enter zero if you are starting from nothing and relying entirely on contributions.

  2. 02

    Set the regular contribution

    Type the amount added at the end of each compounding period. With monthly compounding selected, this is a monthly contribution.

  3. 03

    Enter the return and the timeframe

    Type the expected annual rate and the number of years. Use a nominal annual rate; the calculator converts it to the periodic rate itself.

  4. 04

    Choose a compounding frequency

    Select annual, semi-annual, quarterly, monthly or daily compounding to match how the account credits interest.

  5. 05

    Read the split

    The result strip shows the final balance. The rows beneath separate the money you contributed from the interest the account generated.

The formula

A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
A
The final balance after t years.
P
The starting principal.
r
The annual rate as a decimal — 7% is entered as 0.07.
n
The number of compounding periods per year.
t
The number of years the money is invested.
PMT
The amount added at the end of each compounding period.

The second term is the future value of an ordinary annuity, which assumes each contribution is made at the end of the period. Contributions made at the start of each period earn one extra period of growth and are worth (1 + r/n) times more.

Worked example

Starting amount
$5,000
Added each month
$300
Annual return
7%
Years
20
Compounding
Monthly
Result
$176,472

The periodic rate r/n is 0.07 ÷ 12 = 0.00583333, and nt is 240 periods. The growth factor (1.00583333)^240 equals 4.03874. The starting $5,000 grows to 5,000 × 4.03874 = $20,194. The contributions form an annuity worth 300 × (4.03874 − 1) ÷ 0.00583333 = $156,278. Adding the two gives $176,472. Total money contributed is $5,000 + $72,000 = $77,000, so $99,472 — 56% of the final balance — is compound interest.

Frequently asked questions

What is the compound interest formula?

The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years. Regular contributions add the annuity term PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)].

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal, so it grows linearly: $10,000 at 5% earns $500 every year indefinitely. Compound interest is calculated on principal plus accrued interest, so it grows exponentially. Over 30 years at 5%, simple interest turns $10,000 into $25,000, while annual compounding turns it into $43,219.

How does compounding frequency change the result?

More frequent compounding produces a higher effective yield from the same nominal rate. $10,000 at 12% for one year grows to $11,200 with annual compounding, $11,268 with monthly compounding and $11,275 with daily compounding. The gain shrinks with each step up in frequency, converging on the continuous limit Pe^(rt), which gives $11,275.

What is the rule of 72?

The rule of 72 estimates how long an investment takes to double: divide 72 by the annual percentage rate. At 8%, doubling takes roughly 72 ÷ 8 = 9 years, against an exact figure of 9.01 years. The approximation is accurate to within a few months for rates between about 4% and 15%.

What is APY and how does it differ from the interest rate?

The annual percentage yield expresses what a nominal rate actually earns once compounding is accounted for, using APY = (1 + r/n)ⁿ − 1. A 12% nominal rate compounded monthly has an APY of 12.68%. In the United States, Regulation DD requires deposit accounts to advertise APY specifically so that accounts with different compounding schedules compare directly.

Does this calculator account for inflation, tax or fees?

No. The result is a nominal, pre-tax, pre-fee figure. To approximate real purchasing power, subtract expected inflation from the return rate before entering it — a 7% return with 3% inflation is roughly a 4% real rate. Investment fees should be deducted from the rate in the same way.

Is a 7% annual return a reasonable assumption?

Seven percent is a commonly used long-run estimate for a diversified equity portfolio after inflation, derived from roughly a century of US market history. It is an average across decades, not a guarantee for any single year — equity markets routinely deliver returns between −40% and +40% annually. Cash and bond assumptions should be considerably lower.

Sources

Last reviewed: · Formula and sources verified by Syed Aqeel Ahmad Gillani. See the methodology for how every calculation is derived.

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