Compound Interest Calculator
See how investments grow with the power of compounding — with the standard A = P(1+r/n)^(nt) formula.
About the Compound Interest Calculator
The compound interest calculator projects how an initial sum — and optional monthly contributions — grows over time when interest is reinvested rather than withdrawn. Albert Einstein is often (though apocryphally) credited with calling compound interest "the eighth wonder of the world," but the underlying mathematics is genuinely powerful: returns earn returns, and the growth curve bends upward as time passes. This tool makes that curve visible in dollar terms.
Compound interest is the foundation of long-term investing. The same mechanism that grows a savings account also grows retirement accounts, dividend-reinvestment plans, and reinvested bond coupons. The Securities and Exchange Commission's Investor.gov resource describes compound growth as "interest earned on interest" and stresses that the earlier you start, the more dramatic the effect — a point this calculator makes by letting you vary the time period and immediately see the future value change.
The tool supports five compounding frequencies — annual, semi-annual, quarterly, monthly, and daily — and computes the Effective Annual Rate (EAR) so you can compare rates quoted with different compounding conventions. A 7.0% nominal rate compounded monthly has an EAR of 7.2295%, which is what you actually earn over a year. This distinction matters when comparing a savings account paying 7.0% monthly against a bond paying 7.1% semi-annually.
The optional monthly contribution field lets you model the impact of regular saving on top of the initial principal. Many real-world investment scenarios — retirement accounts, education savings plans, dollar-cost-averaging into index funds — involve both a starting balance and ongoing contributions, and the future value of an annuity formula handles the contribution stream separately from the lump-sum compound growth.
How It Works
The compound growth of a lump sum uses the standard compound interest formula:
A = P x (1 + r/n)^(n x t)
where:
P = principal
r = annual nominal rate (as decimal)
n = compounding periods per year
t = yearsThe future value of regular monthly contributions uses the future value of an ordinary annuity formula, with the contribution rate adjusted to monthly:
FV_contrib = PMT x (((1 + r/12)^(12 x t) - 1) / (r/12))
where PMT = monthly contribution, r/12 = monthly rateTotal future value is the sum of the lump-sum compound growth and the contribution stream's future value. The Effective Annual Rate (EAR) converts the nominal rate with a given compounding frequency into an equivalent annual rate:
EAR = (1 + r/n)^n - 1This lets you compare a 7.0% rate compounded monthly (EAR 7.2295%) against a 7.1% rate compounded semi-annually (EAR 7.2260%) on equal footing — the monthly-compounded rate actually wins by a hair. The Rule of 72 estimates the doubling time of an investment at a given rate:
Years to double = 72 / annual_rate_in_percent
(e.g. 72 / 7 = 10.3 years to double at 7% per year)The Rule of 72 is exact for 7.85% and within 1% of the true doubling time across the 4% to 12% range. It is a sanity check, not a substitute for the precise formula.
Worked Examples
Using the default inputs: $10,000 principal at 7.0% nominal compounded monthly for 20 years with $200 monthly contribution. Lump-sum growth: 10000 x (1 + 0.07/12)^(12 x 20) = 10000 x 4.0387 = $40,387. Contribution stream FV: 200 x ((1.005833^240 - 1) / 0.005833) = $104,185. Total = $144,573. Of that, principal + contributions = $58,000 and interest earned = $86,573. EAR = (1.005833)^12 - 1 = 7.2290%. Rule of 72: 72 / 7 = 10.29 years to double the initial $10,000.
Now consider the same $10,000 at 7.0% compounded monthly for 40 years instead of 20. Lump-sum growth: 10000 x (1.005833)^480 = $163,114. Doubling the time more than quadruples the lump-sum value — this is the upward bend of compound growth. If you also contribute $200/month for 40 years: contribution FV = 200 x ((1.005833^480 - 1) / 0.005833) = $524,963. Total = $688,077, of which $106,000 is deposits ($10,000 starting + $96,000 monthly) and $582,077 is interest.
For a savings account with $5,000 at 4.5% nominal, the EAR comparison across frequencies: annual = 4.5000%, semi-annual = 4.5506%, quarterly = 4.5765%, monthly = 4.5940%, daily = 4.6025%. The difference between annual and daily compounding at 4.5% is about 0.10 percentage points per year — small in any single year, but over 30 years it compounds to roughly $565 extra on a $5,000 starting balance ($19,291 vs. $18,727).
Rule of 72 sanity check: at 6% per year, doubling time = 72/6 = 12 years. Verify: $1,000 x (1.06)^12 = $2,012.20, indeed just over double. At 9%, doubling time = 72/9 = 8 years; verify $1,000 x (1.09)^8 = $1,992.56. At 3%, doubling = 72/3 = 24 years; verify $1,000 x (1.03)^24 = $2,032.79. The rule over-estimates slightly at low rates and under-estimates slightly at high rates, which is why it is a sanity check rather than a precise calculation.
When to Use This Tool
Use the compound interest calculator when you need to:
- Project the future value of a savings account, CD, or money market fund.
- Model retirement contributions starting from a current balance.
- Compare rates quoted with different compounding frequencies using the EAR.
- Estimate how long it takes for an investment to double at a given rate.
- Demonstrate the long-term cost of cash sitting idle versus invested.
- Plan education savings for a child over 18 years.
- Visualise why small rate differences compound into large dollar differences over decades.
Limitations & Disclaimer
This calculator uses nominal compound interest math and does not adjust for inflation, taxes, fees, investment risk, or market volatility. Real investment returns vary year to year and may be negative in any given period. Past performance is not indicative of future results. The monthly contribution formula assumes contributions at the end of each month (ordinary annuity). For tax-advantaged or taxable accounts, the after-tax return may differ materially. For investment decisions, consult a licensed financial advisor. See our disclaimer for full details.
Frequently Asked Questions
What is the difference between APR, APY, and EAR?
APR (Annual Percentage Rate) is the nominal yearly rate, often used for loans. APY (Annual Percentage Yield) and EAR (Effective Annual Rate) are the same thing — the actual yearly return after compounding. A 12.0% APR compounded monthly has an APY/EAR of 12.6825%. The Truth in Savings Act (12 CFR Part 1030) requires U.S. banks to disclose APY on deposit accounts, while the Truth in Lending Act (15 U.S.C. Sec. 1601) requires APR disclosure on loans.
Why does daily compounding give only slightly more than monthly?
Because the formula <code>(1 + r/n)^n</code> converges to <code>e^r</code> as n grows, and the difference between monthly and daily is small. At 7.0%, monthly compounding gives EAR 7.2295%, daily gives 7.2501%, and continuous (e^0.07) gives 7.2508%. The jump from annual to monthly is much larger than from monthly to continuous, which is why compounding frequency matters less than getting started early.
Does this calculator account for inflation?
No. The future value is in nominal dollars — the actual dollar amount your balance will show. To convert to real (inflation-adjusted) dollars, subtract the expected inflation rate from the investment rate before entering it. For example, with 7.0% nominal return and 3.0% expected inflation, the real return is approximately 4.0% (more precisely, 1.07 / 1.03 - 1 = 3.88%).
Is the monthly contribution compounded monthly even if I select annual compounding?
Yes. Contributions are made monthly, so the calculator compounds the contribution stream monthly regardless of the chosen frequency for the lump-sum principal. This matches how real monthly savings behave in practice. The lump-sum portion uses the selected compounding frequency.
What is the Rule of 72 and how accurate is it?
The Rule of 72 estimates doubling time as <code>72 / annual_rate_percent</code>. At 7%, it estimates 10.3 years, while the exact value is <code>ln(2)/ln(1.07) = 10.24 years</code>. The rule is within 1% of the true doubling time across the 4% to 12% range, and is exact at about 7.85%. It is a sanity check, not a substitute for precise calculation.
How are taxes handled?
They are not. This calculator shows pre-tax growth. Interest income is generally taxable as ordinary income in the year it is credited, per IRC Sec. 61. For tax-deferred accounts like traditional IRAs or 401(k)s, the pre-tax figure is what compounds until withdrawal. For taxable accounts, you must reduce the rate by your marginal tax rate to estimate after-tax growth — for example, a 7% return at a 24% marginal rate gives roughly 5.32% after tax.
Last updated: September 9, 2026 · Author: HT99 Tools Editorial Team