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Free Compound Interest Calculator

See how your money grows with compound interest and monthly contributions. No signup, no ads tracking.

Quick start
Future value
$691,150
after 30 years
Principal $10,000 · 1%
Contributions $180,000 · 26%
Interest earned $501,150 · 73%
Total invested
$190,000
Interest earned
$501,150
APY
7.23%
Doubles every
10.3 yrs
Rule of 72: at 7.00%, your money doubles roughly every 10.3 years
What if the rate changes?
5%per year
$460,807
your rate
7%per year
$691,150
9%per year
$1,062,678
Balance over time
Annual composition
Principal
Contributions
Interest
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How compound interest works

Compound interest means earning interest on your interest. When interest is added to your balance, that larger balance earns more interest in the next period — creating a self-reinforcing growth cycle. The formula is FV = P(1 + r/n)^(nt), where P is principal, r is the annual rate, n is compounding frequency, and t is years.

Monthly contributions dramatically amplify this effect. Each new dollar you add immediately begins compounding. The earlier you start contributing — even small amounts — the more time each dollar has to compound, producing results that can seem almost magical over long time horizons.

What does $10,000 grow to at different rates?

With no additional contributions, monthly compounding, over 20 years:

Rate5 years10 years20 years30 years
4%$12,210$14,888$22,167$33,024
6%$13,488$18,194$33,102$60,226
8%$14,898$22,196$49,268$109,357
10%$16,453$27,070$73,281$198,374

How compound interest with monthly contributions works

Adding $500/month to a $10,000 initial investment at 7% for 30 years: without contributions, the $10,000 grows to $76,123. With $500/month contributions, the balance reaches $613,543 — your $10,000 plus $180,000 in contributions earned $423,543 in compound interest.

The key insight: even though the total contributions ($180,000) are almost 2× the initial investment ($10,000), the interest earned ($423,543) dwarfs both. This is because every new contribution immediately starts compounding alongside the original principal.

The Rule of 72 — how fast does your money double?

Divide 72 by your annual interest rate to estimate the doubling time. At 6% → 12 years. At 8% → 9 years. At 10% → 7.2 years. This rule is accurate within 1% for rates between 2% and 15%. The exact formula is t = ln(2) / ln(1+r). This calculator shows your doubling time automatically in the results panel.

Daily vs monthly vs annual compounding: does it matter?

On $10,000 at 7% over 30 years: annual compounding → $76,123. Monthly compounding → $81,745. Daily compounding → $81,822. The difference between monthly and daily is just $77 over 30 years — negligible. The compounding frequency matters far less than the rate itself and how long you stay invested. Monthly compounding is standard for most savings and investment accounts.

Frequently asked questions

Everything you need to know about compound interest.

Compound interest terms explained

Principal
The initial amount of money invested or deposited before any interest is added.
Compound Interest
Interest calculated on both the initial principal and all accumulated interest from prior periods — causing exponential rather than linear growth.
APY (Annual Percentage Yield)
The effective annual return after accounting for compounding frequency. Always higher than APR when compounding more than once per year.
APR (Annual Percentage Rate)
The nominal annual interest rate stated before compounding. The rate used in the compound interest formula as the base input.
Compounding Frequency
How often interest is calculated and added to the balance. Daily compounding earns slightly more than monthly, which earns slightly more than annual.
CAGR (Compound Annual Growth Rate)
The constant annual rate that would take an investment from its starting value to its ending value over a given period, accounting for compounding.
Rule of 72
A quick approximation: divide 72 by the annual interest rate to estimate years required to double your money. At 6%: ~12 years. At 9%: ~8 years.
Future Value (FV)
The projected value of an investment at a specific date in the future, given an assumed rate of return and compounding schedule.

The compound interest formula

FV = P(1 + r/n)^(nt) + PMT × [(1 + r/n)^(nt) − 1] / (r/n)
FV
Future value — the ending balance
P
Principal — the starting amount
r
Annual interest rate (as a decimal, e.g. 0.07 for 7%)
n
Compounding frequency per year (12 for monthly, 365 for daily)
t
Time in years
PMT
Periodic contribution amount (monthly deposit)
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Results are illustrative only and do not constitute financial advice. Actual investment returns vary and are not guaranteed. Consult a qualified financial advisor before making investment decisions.

Why compound interest is called the eighth wonder of the world

Compound interest earns returns on both your original principal and the interest already accumulated. This seemingly small difference from simple interest produces dramatically different outcomes over time. $10,000 at 7% simple interest for 30 years grows to $31,000. The same $10,000 at 7% compound interest grows to $76,123 — more than twice as much, from the same initial investment and the same rate, simply because the interest compounds rather than staying flat.

The formula is FV = P(1 + r/n)^(nt), where P is principal, r is the annual rate, n is compounding frequency per year, and t is time in years. Daily compounding versus annual compounding on the same nominal rate produces a slightly higher effective annual yield (APY). At 6% nominal, monthly compounding gives an APY of 6.168%, while annual compounding gives exactly 6%.

The Rule of 72

The Rule of 72 is a mental math shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in about 12 years. At 9%, about 8 years. At 4%, about 18 years. The rule is accurate within 1% for rates between 2% and 15%, making it a reliable first-order estimate without a calculator.

The rule also works in reverse: if you need your money to double in 10 years, you need approximately a 7.2% annual return. It is one of the most useful tools in personal finance for quickly evaluating whether an investment goal is realistic given a realistic rate assumption.

How monthly contributions change the outcome

The most underestimated variable in long-term investing is not the interest rate — it is the ongoing contribution. $10,000 invested at 7% for 30 years with no further contributions grows to $76,123. Add $300 per month and the ending balance is $378,000 — nearly 5× more — from $108,000 in total contributions that earned $194,000 in compound interest on top.

Time matters more than the contribution amount in the early years. A person who invests $5,000 at age 25 and adds nothing will have more at age 65 than someone who invests $5,000 at age 35 and adds $100/month for the following 30 years — the 10-year head start compounds faster than the ongoing contributions can catch up.