Compound Interest Calculator
Grow a lump sum plus regular contributions at any compounding frequency.
Reviewed by the Calculation Machine team · Updated 24 October 2026 · How we check our maths
Your values
ⓘ Live results
- Future value
- $170,619.05
- Total contributed
- $70,000.00
- Interest earned
- $100,619.05
- Growth multiple
- 2.44×
Quick answer
Compound interest is interest earned on both your original money and the interest already added to it. A lump sum grows as A = P(1 + r/n)^(nt), where r is the annual rate, n the compounding periods per year and t the years; regular deposits grow on top. $10,000 plus $250 a month at 7% compounded monthly for 20 years reaches $170,619.05, of which $100,619.05 is interest.
What the Compound Interest calculator does
This calculator projects the future value of savings or investments that compound. Enter a starting amount, a monthly contribution, an annual rate of return, the number of years and how often interest compounds. It returns the final balance, the total you paid in, the interest earned and how many times your contributions have multiplied.
Use it for a savings account, a brokerage or retirement account, or to show how much starting early matters. For a bank account, enter the stated interest rate. For investments, the rate is an assumption, not a promise: stock returns vary widely from year to year, so try a cautious rate as well as an optimistic one.
The figures are before tax, fees and inflation. To see the result in today's money, rerun it with your return minus expected inflation, or check the inflation calculator. For a quick doubling-time estimate, the rule of 72 divides 72 by the rate.
The formula
FV = P(1 + r/n)^(nt) + PMT × [(1 + i)^(12t) − 1] ÷ i, where i = (1 + r/n)^(n/12) − 1
| Symbol | Meaning | Unit |
|---|---|---|
| P | Starting amount (principal) | $ |
| PMT | Amount added at the end of each month | $ |
| r | Annual interest rate or return, as a decimal | — |
| n | Compounding periods per year (1, 4, 12 or 365) | per year |
| t | Number of years | years |
| i | Equivalent monthly growth rate at the chosen compounding frequency | decimal |
The first term is the textbook compound interest formula for a lump sum. The second is the future value of an ordinary annuity: monthly deposits made at the end of each month, each growing at the monthly rate that matches the chosen compounding. Deposits made at the start of each month would end slightly higher.
The formula assumes a constant rate. Real investment returns arrive unevenly, so a portfolio averaging 7% will not follow this smooth curve, and the order of good and bad years matters once you start withdrawing.
Worked examples
$500 a month for 30 years
Starting from zero, investing $500 a month at an assumed 7% return, compounded monthly, for 30 years.
Inputs
- Starting amount0 $
- Monthly contribution500 $
- Annual return7 %
- Years30 years
- CompoundingMonthly
Result
- Future value$609,985.50
- Total contributed$180,000.00
- Interest earned$429,985.50
- Growth multiple3.39×
$180,000 of deposits grows to $609,985.50. The same $500 a month for 20 years reaches about $260,463, so the last 10 years add more than the first 20 years of saving combined.
Lump sum left alone for 10 years
A one-off $10,000 at 7% a year, compounded yearly, with nothing added.
Inputs
- Starting amount10000 $
- Monthly contribution0 $
- Annual return7 %
- Years10 years
- CompoundingYearly
Result
- Future value$19,671.51
- Total contributed$10,000.00
- Interest earned$9,671.51
- Growth multiple1.97×
The balance grows to $19,671.51, close to doubling, as the rule of 72 predicts (72 ÷ 7 ≈ 10.3 years). Daily compounding at the same rate would give $20,136.18.
High-yield savings account
$20,000 in a savings account at 4.5% compounded daily, adding $100 a month for 5 years.
Inputs
- Starting amount20000 $
- Monthly contribution100 $
- Annual return4.5 %
- Years5 years
- CompoundingDaily
Result
- Future value$31,762.06
- Total contributed$26,000.00
- Interest earned$5,762.06
- Growth multiple1.22×
The account reaches $31,762.06, with $5,762.06 of interest. Savings rates change over time, so treat a five-year projection as an estimate unless the rate is locked, as in a CD.
How much compounding frequency matters
More frequent compounding adds a little each period, but the gains shrink quickly. The rate and the number of years matter much more than whether interest is added monthly or daily.
| Compounding | Effective annual rate | Balance after 10 years |
|---|---|---|
| Yearly | 7.00% | $19,671.51 |
| Quarterly | 7.19% | $20,015.97 |
| Monthly | 7.23% | $20,096.61 |
| Daily | 7.25% | $20,136.18 |
Choosing a realistic rate
- Savings accounts and CDs: use the stated APY with yearly compounding, or the interest rate with the bank's compounding frequency. For fixed-term deposits, the CD calculator handles terms in months.
- Bonds: use the yield to maturity of the bonds or fund you hold.
- Stocks: broad US stock indexes have historically returned roughly 10% a year before inflation over very long periods, but with large swings and decades well below average. Many planners use 5% to 7% for long-range projections to leave a margin.
- After fees: subtract fund expense ratios and advisory fees from the rate; a 1% annual fee compounds against you just as returns compound for you.
Common mistakes when projecting growth
- Ignoring inflation: $609,986 in 30 years will buy much less than it does today. Use a real return (rate minus inflation) to see purchasing power.
- Ignoring taxes: interest in a taxable account is taxed each year, which slows compounding. Tax-advantaged accounts such as a 401(k) or IRA let it compound untaxed until withdrawal, or permanently in a Roth.
- Assuming a fixed return is guaranteed: for investments, run a low, middle and high rate to see a range rather than one number.
- Stopping contributions early: in most long projections, regular deposits make up a large share of the final balance.
How to use the Compound Interest Calculator
- 1Enter what you have saved or invested today as the starting amount (0 if starting fresh).
- 2Enter how much you will add each month; the calculator assumes deposits at month end.
- 3Enter the annual interest rate or expected return as a percentage.
- 4Enter the number of years and pick the compounding frequency your account uses.
- 5Read the future value, then compare total contributed with interest earned.
Frequently asked questions
How do you calculate compound interest?
Multiply the principal by (1 + rate ÷ n) raised to the power n × years, where n is compounding periods per year. For $5,000 at 5% compounded yearly for 10 years: 5,000 × 1.05^10 = $8,144.47.
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal, while compound interest is also paid on interest already earned. Over long periods the gap becomes large; compare them with the simple interest calculator.
How long does it take money to double with compound interest?
Divide 72 by the annual rate for a close estimate. At 6% money doubles in about 12 years; at 9%, in about 8 years.
Is daily compounding better than monthly?
Slightly. At 7%, daily compounding gives an effective rate of about 7.25% against 7.23% for monthly, a difference of roughly $40 on $10,000 over 10 years.
Does the stock market pay compound interest?
Not interest as such, but reinvested dividends and price growth compound in the same way. The difference is that the return varies each year instead of being fixed.
References
- Compound Interest Calculator – Investor.gov — US Securities and Exchange Commission
- Truth in Savings Act (Regulation DD) – Annual Percentage Yield — Consumer Financial Protection Bureau
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Last reviewed: October 24, 2026
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