Compound Interest Calculator
Last Updated:
See exactly how your money grows with compound interest: pick a compounding frequency, from daily to annual, and watch what time does to the balance.
Quick answer: Compound interest grows your money using A = P(1 + r/n)^(nt), where interest earns interest on top of interest. $10,000 at 8% compounded monthly reaches $49,268 after 20 years with no further deposits, more than 4.9× the original amount, entirely from compounding (formula per standard financial mathematics).
📊 Show Year-by-Year Schedule
| Year | Deposits | Withdrawals | Interest | Balance |
|---|
📐 Compound Interest Formula
A = $10,000 × (1 + 0.08/12)^(12×20)
A = $10,000 × (1.006667)^240
A = $10,000 × 4.9268 = $49,268
How to Use the Compound Interest Calculator
Enter your starting principal
Input your initial investment or savings balance. Even a modest starting amount compounds significantly over long horizons.
Set a monthly contribution
Add a regular monthly contribution. Pairing a starting balance with steady contributions grows money far faster than either one alone.
Choose compounding frequency
Daily compounding (standard for savings accounts) produces slightly more interest than annual. The difference is small but adds up over decades.
Adjust the time horizon
Compare 10, 20, and 30 year outcomes. The curve bends sharply upward in later years; long time horizons are compound interest's biggest lever.
Add an optional inflation rate
Enter an expected annual inflation rate to see the future value in today's purchasing power alongside the nominal figure.
Add optional raises, withdrawals or a target
Enter an annual contribution increase to model a yearly raise, a monthly withdrawal and how many years to wait before it starts, or a target balance to see how long it takes to reach it. Choose whether deposits land at the end or the start of each period.
Read the year-by-year schedule
Open the schedule under the results to see each year's deposits, withdrawals, interest and ending balance.
What Is Compound Interest and How Does It Work?
Compound interest is calculated on both your original principal and the interest that principal has already earned. Einstein is often credited with calling it the "eighth wonder of the world." He probably never said it, but the math backs up the reputation: interest earns interest, which earns more interest, and wealth compounds faster the longer you leave it alone.
Formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate, n is the compounding frequency, and t is the time in years.
Does Compounding Frequency Actually Matter?
| Compounding | Times/Year | $10,000 at 5% after 10 years |
|---|---|---|
| Annually | 1 | $16,289 |
| Quarterly | 4 | $16,436 |
| Monthly | 12 | $16,470 |
| Weekly | 52 | $16,483 |
| Daily | 365 | $16,487 |
| Continuous | no limit | $16,487 |
Daily compounding earns about $200 more than annual compounding over 10 years on $10,000. That's real money on larger sums and longer timeframes. Most savings and investment accounts compound daily or monthly by default.
Continuous compounding, where interest is compounded continuously, is the limit as the number of periods grows without end, and it uses a different formula: A = P × e^(rt), where e is about 2.71828. For $10,000 at 5% over 10 years that gives $16,487.21, only about 56 cents more than daily compounding ($16,486.65). The calculator offers daily, monthly, quarterly, semi-annual and annual compounding. Weekly and continuous appear in the table for comparison, and the difference beyond daily is pennies.
The Rule of 72: Quick Mental Math for Doubling Time
The Rule of 72 estimates how long it takes to double your money: divide 72 by the annual interest rate. At 6%, that's 72 ÷ 6 = 12 years. At 8%, 9 years. At 4%, 18 years. It lands within about 5.5% of the exact doubling time for any rate from 4% to 20%, and gets closest near 8%. That range covers most real-world savings and investment scenarios.
Compound Interest vs Simple Interest
Simple interest is calculated only on the principal: I = P × r × t. Compound interest calculates on principal plus whatever interest has already accrued. Over a year or two the gap is small. Over decades, it's enormous. $10,000 at 7% simple interest for 30 years grows to $31,000. At 7% compound interest, it reaches $76,123, more than double. Run the numbers on a simple-interest loan or bond directly in the Simple Interest Calculator.
How Regular Contributions Change the Math
Adding a regular monthly or annual contribution accelerates growth sharply. Investing $500/month at 7% for 30 years (monthly compounding, matching the calculator's own default above) results in about $610,000, from just $180,000 in total contributions. The remaining roughly $430,000 came entirely from compound interest. If you start 10 years earlier, the final number can more than double. Time in the market, not timing the market, is what does the heavy lifting. Deciding between a 15-year and 30-year mortgage comes down to the same trade-off: a smaller required payment freed up to invest versus a guaranteed, debt-free return. Compare the two directly in the 15 vs 30 Year Mortgage Calculator.
Compound Interest Formula With Monthly Contributions
Add the future value of a stream of deposits to the lump-sum formula: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)], where PMT is the deposit made each compounding period. For $10,000 at 5% with $200 a month for ten years, compounded monthly, the lump sum grows to $16,470.09 and the deposits grow to $31,056.46, a total of $47,526.55.
The calculator handles your monthly contribution in one specific way: it splits the year's contributions evenly across the compounding periods and, with the default timing, deposits each share at the end of its period. With monthly compounding that is $200 at the end of every month. With annual compounding the whole $2,400 lands once, at year-end, so it earns less than 12 separate deposits would. Choose Start of each period under Contribution Timing and each deposit goes in before that period's interest is earned, which earns slightly more.
Yearly Contributions vs Monthly Contributions
The same money paid in at a different rhythm ends up in a different place. Take $60,000 contributed over 10 years at 5%, with no starting balance:
| How you contribute | Compounding | Balance after 10 years |
|---|---|---|
| $6,000 once a year, at year-end | Annually | $75,467 |
| $500 every month, at month-end | Monthly | $77,641 |
Monthly deposits finish $2,174 ahead because each one starts earning sooner and interest compounds twelve times a year instead of once. To reproduce both rows, enter $0 as the principal, 5% and 10 years, $500 as the monthly contribution, then switch the frequency between Annually and Monthly.
Increasing Contributions: What a Yearly Raise Adds
A yearly raise adds up. Start at $200 a month and raise it 3% every year for ten years, at 5% compounded monthly with no starting balance: the balance reaches $35,173 from $27,513 contributed. The same $200 held flat gives $31,056 from $24,000 contributed. The raise adds $4,117 to the final balance. Each year's monthly deposit is 3% higher than the previous year's, and every deposit is paid at the end of its month. To reproduce it, enter $0 as the principal, 5% and 10 years, $200 as the monthly contribution and 3% as the Annual Contribution Increase. The raise starts in year 2, and the schedule shows each year's deposits.
Withdrawals, Timing and Target Balance
Enter a monthly withdrawal and the number of years to wait before it starts. The calculator splits the year's withdrawals across the compounding periods and takes each one at the same point in the period as your deposits, at the end or the start depending on the timing you chose. The balance never goes below zero: if the money runs out, the results say which year. Withdrawals stay flat. They are not raised for inflation, and no tax or fees come out.
Enter a target balance and the calculator keeps compounding past your time period, up to a total of 100 years, until the balance reaches it, then reports the time in years and months. The interest split divides total interest in two: what your starting balance earns on its own, and the net interest on contributions, which is what your deposits earn minus what the money you withdrew would otherwise have earned. With withdrawals and few deposits, that second figure can be negative.
How to Calculate Compound Interest in Excel and Google Sheets
Both programs use the same function, FV(rate, periods, payment, present value, type). Enter the rate per compounding period and the number of compounding periods, and enter money you pay in as negative numbers. For $10,000 plus $200 a month at 5% for ten years, compounded monthly:
=FV(0.05/12, 10*12, -200, -10000)That returns $47,526.55, matching the formula above. An optional fifth argument (type) of 1 puts each deposit at the start of its period instead of the end. To see what is left after taking money out, make the payment positive.
=FV(0.05/12, 10*12, 500, -100000)That returns $87,059.81, the balance left after ten years of $500 monthly withdrawals. To get the same result in the calculator, enter $100,000 as the principal, 5% and 10 years, leave the frequency on Monthly, and enter $500 as the Monthly Withdrawal; it shows the balance as $87,060. Microsoft documents the arguments and the sign convention for Excel; Google Sheets takes the same arguments in the same order.
How Compounding Frequency Changes Your Return: Worked Example
Deposit $10,000 at a 5% nominal annual rate for 10 years and vary only how often interest compounds, using A = P(1 + r/n)ⁿᵗ.
- Annual (n=1): $10,000 × 1.05¹⁰ = $16,288.95
- Monthly (n=12): $10,000 × (1 + 0.05/12)¹²⁰ = $16,470.09
- Daily (n=365): $10,000 × (1 + 0.05/365)³⁶⁵⁰ = $16,486.65
Moving from annual to daily compounding adds $197.70 over ten years on the same nominal rate. Real, but modest. It's also why comparing accounts by nominal rate alone can mislead: a 5.00% account compounded daily slightly out-earns a 5.05% account compounded annually, exactly what APY (annual percentage yield) exists to normalize.
How Much Do Regular Contributions Change the Outcome?
What does adding $200 a month do to the ten-year total?
Adding $200 a month to the $10,000 lump sum lifts the ten-year total from $16,470 to $47,527, and $31,056 of that comes from the deposits and the interest they earn. The deposits supply most of the total, which is the central lesson of long-horizon compounding: consistent contributions usually beat chasing an extra percentage point of return.
Is the Rule of 72 accurate enough to use?
Dividing 72 by the rate estimates doubling time: at 7%, 72 ÷ 7 ≈ 10.3 years. The exact answer from ln(2) ÷ ln(1.07) is 10.24 years. The rule lands within about 1% of the exact answer between 6% and 10%, the range typical of long-term investing, which is why it's reliable for a quick mental check without reaching for a calculator.
Why does starting a decade earlier matter more than the rate?
A one-time $10,000 deposit at 7% for 40 years grows to about $149,745. The same deposit for 30 years, started a decade later, reaches only about $76,123, about half, despite an identical rate. The missing decade of compounding causes that gap, not a worse return, which is why the calculator's time-horizon field usually moves your projected total more than the rate field does. That's the power of an extra decade of compounding. The calculator can also draw a balance down: enter a monthly withdrawal and how many years to wait before it starts. To plan a whole retirement around a balance like this, the Retirement Calculator picks up from here.
Frequently Asked Questions
Sources & Methodology
The compound interest formula follows standard financial mathematics. For further reading and independent verification, see: