Money
Compound Interest Calculator
Enter a starting principal, an annual interest rate, a time horizon, a compounding frequency, and an optional monthly contribution. The calculator returns the future balance, the total you contributed, and how much of the final balance is interest.
The amount you start with. · e.g. 10,000
Nominal annual rate. · e.g. 7
e.g. 20
Compounding frequency
Added at the end of each month. · e.g. 100
Future balance after 20 years
$92,480.05
Contributed $34,000.00 · interest earned $58,480.05
Growth summary (first three + final year)
- Year 1$11,962.16
- Year 2$14,066.16
- Year 3$16,322.27
- Year 20$92,480.05
Estimate only. Real returns, taxes, fees, and contribution timing can change the final number.
Examples
$10,000 at 7% monthly · 20 yr · +$100/mo
≈ $92,480 balance · $58,480 interest
$1,000 at 5% monthly · 10 yr · no contribution
≈ $1,647 balance · $647 interest
$10,000 at 7% annually · 20 yr · +$100/mo
≈ $89,450 balance · $55,450 interest
$10,000 at 7% continuously · 20 yr · +$100/mo
≈ $92,774 balance · $58,774 interest
How it works
For a one-time deposit with no recurring contributions, the classic compound interest formula gives the future balance directly. When you also add a monthly contribution, the calculator converts the chosen compounding frequency into an effective monthly rate and applies the future value of an annuity formula on top.
Compound interest (no recurring contributions)
A = P × (1 + r/n)^(n·t)
The parts
- A = future balance
- P = starting principal
- r = annual interest rate (decimal)
- n = compounding periods per year
- t = time in years
Continuous compounding
A = P × e^(r·t)
With monthly contributions
r_m = (1 + r/n)^(n/12) − 1
A = P × (1 + r_m)^(12·t) + PMT × ((1 + r_m)^(12·t) − 1) / r_m
The first term grows the principal. The second term is the future value of the monthly contribution stream.
What the calculator does
You enter the starting principal, the annual interest rate, the time horizon, a compounding frequency, and an optional monthly contribution. The calculator returns the future balance, total contributions, and the interest portion of the final balance. A short year-by-year preview shows the first three years and the final year so you can see how the balance scales.
Why compounding frequency matters
At the same nominal annual rate, more frequent compounding produces a slightly higher final balance. For 7% compounded annually, $10,000 over 20 years grows to about $38,697. For 7% compounded monthly the same deposit grows to about $40,387. The gap widens with rate, time, and balance, but past monthly the additional gains are small.
How monthly contributions are modeled
Each contribution is added at the end of the month and compounds from then on. The calculator first converts the chosen compounding frequency into an effective monthly rate, then runs the standard future value of an annuity formula on that rate. This means contributions and compounding line up cleanly even when the compounding frequency is annual, quarterly, daily, or continuous.
Worked example
Starting principal $10,000, annual rate 7%, monthly compounding, 20 years, monthly contribution $100.
- Effective monthly rate: 7% ÷ 12 ≈ 0.5833%
- Total months: 20 × 12 = 240
- Principal future value: 10,000 × (1.00583)^240 ≈ $40,387
- Annuity future value: 100 × ((1.00583)^240 − 1) ÷ 0.00583 ≈ $52,093
- Future balance: ≈ $92,480
- Total contributions: 10,000 + 100 × 240 = $34,000
- Interest earned: ≈ $58,480
About 63% of the final balance is interest, which is the practical reason compounding matters so much over long time horizons.
Compound interest vs simple interest
Simple interest is calculated only on the original principal, so it grows linearly. Compound interest is calculated on principal plus accumulated interest, so it grows exponentially. Over short periods the two are close; over decades, compound interest pulls far ahead.
Common mistakes
- Treating APR and APY as the same number. APY is the effective rate after compounding; APR is the nominal rate.
- Comparing two scenarios with different compounding frequencies as if they were the same. Convert to APY (or use the calculator) before judging.
- Forgetting inflation. A nominal balance is not the same as purchasing power. Subtract an expected inflation rate from the annual rate to estimate the real return.
- Trusting a single rate to hold for decades. Markets fluctuate; use the projection as a planning estimate, not a forecast.
- Ignoring fees. Investment fees compound the same way returns do. A 1% annual fee over 30 years takes a real bite out of the final balance.
Related tools
- 401k calculator for retirement scenarios that include salary growth and employer match.
- Roth IRA calculator for projecting an individual after-tax retirement account.
- Loan calculator for compound interest on the other side of the ledger.
- Mortgage calculator for principal and interest plus taxes, insurance, PMI, and HOA.
- Car payment calculator for auto loans with sales tax, trade in, and down payment.
- Percentage increase calculator for comparing growth rates side by side.
Disclaimer. This calculator is an estimate for general planning. Actual investment balances can vary based on market returns, fees, taxes, contribution timing, and account rules. It is not investment, tax, or financial advice, and it does not guarantee any return.
Frequently asked questions
Compound interest is interest that earns interest on itself. Each compounding period, the interest accrued is added to the principal, and the next period's interest is calculated on the new, larger balance. Over time the balance grows faster than it would with simple interest.
For a one-time deposit with no recurring contributions, the formula is A = P × (1 + r/n)^(nt). A is the future balance, P is the starting principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the time in years. For continuous compounding, A = P × e^(rt).
It converts the chosen compounding frequency into an effective monthly rate and then applies the standard future value of an annuity formula with that rate. Each contribution is added at the end of the month and compounds from then on. This keeps the math clean across annual, semi-annual, quarterly, monthly, daily, and continuous compounding.
Compounding frequency is how often interest is added to the balance. Higher frequencies pay slightly more because interest starts earning interest sooner. Going from annual to monthly compounding makes a noticeable difference; going from daily to continuous makes almost no difference in everyday situations.
APR (annual percentage rate) is the nominal annual rate without considering compounding. APY (annual percentage yield) is the effective rate after compounding is taken into account. A 6% APR compounded monthly is about 6.17% APY. For investment growth questions, APY is the more honest comparison.
The formula is exact for the inputs you provide. Real returns are not exact. Investment returns vary year to year, fees and taxes reduce the balance, and contribution timing can drift. Use the calculator for planning, not as a guarantee of future returns.
No. The output is in nominal dollars at the projected date. To estimate purchasing power, lower the annual rate by your assumed inflation rate before running the projection. For example, a 7% nominal return at 3% inflation is roughly a 4% real return.
The rule of 72 is a quick mental estimate: at an annual rate of r percent, money doubles in roughly 72 ÷ r years. At 7% it doubles in about 10.3 years; at 4% in about 18 years. It is an approximation of the compound interest formula and is most accurate for rates between 4% and 10%.
Mathematically a negative rate would shrink the balance, but the calculator does not accept negative rates. For modeling losses, see a dedicated investment-loss tool. For loans, the interest is compounding against you, which is exactly the math behind credit card balances and amortized loan payments.
Compound interest math is the same underneath all three. The 401k and Roth IRA calculators wrap it in account-specific framing (employer match, contribution caps, retirement timing). This page is the generic version. Use the dedicated calculators when your scenario fits them.
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