MathBench

Compound Interest Calculator

Enter a starting amount, a monthly contribution, and a rate, and watch what time does: final balance, how much of it is interest, and the growth curve year by year.

Educational estimates only. This calculator is for planning and education. It is not financial, tax, or investment advice, and results may differ from what a lender, broker, or the IRS calculates for your situation. Confirm important decisions with a qualified professional.

Result

—final balance
—total growth earned
—total contributed
—growth ÷ contributions

How this calculator works

The calculator grows your starting amount month by month: each month the balance earns the monthly-equivalent of your annual rate (derived from the compounding frequency you choose), then your contribution is deposited. The chart plots that balance against a dashed line of what you put in. The gap between the two lines is the interest earned so far, and it widens as interest earns interest.

The result panel splits the final balance into contributions and growth, and reports growth as a multiple of what you contributed: the single most motivating number in personal finance. Over long horizons the multiple exceeds 1: the account earned more than you deposited, and every year added at the front of the timeline raises it further.

The formula

FV = P × (1 + r/n)^(n·t)  +  PMT × [ ((1+i)^m − 1) ÷ i ]

i = (1 + r/n)^(n/12) − 1   (monthly-equivalent rate)
m = months, deposits at end of each month

The first term is the textbook compound interest formula for the lump sum. The second is the future value of the stream of deposits (an ordinary annuity). This is the same arithmetic behind the U.S. Securities and Exchange Commission's compound interest calculator at investor.gov. Their site is a good independent place to check any result here.

Worked example

Say you invest $10,000 today and $200 every month at 7%, compounded monthly, for 30 years:

  1. Monthly rate: 7% ÷ 12 = 0.5833% per month
  2. Lump sum: 10,000 × (1.005833)^360 = $81,165
  3. Contributions: 200 × [((1.005833)^360 − 1) ÷ 0.005833] = $243,994
  4. Final balance: $325,159
  5. Of which you deposited $82,000; growth earned: $243,159 (2.97× your money in)

Note what did the heavy lifting: the $200 monthly stream, small as it feels, ends up worth three times the $10,000 head start. Time in the market compounds contributions too.

Assumptions & tips

  • Start ugly, start now. $100 a month from age 25 beats $300 a month from 40 at the same return. The first years of contributions get the most doublings, and no later heroics recover them.
  • Compare APY, not APR. Banks quote whichever looks better. APY already includes compounding, so it's the right number for comparing accounts. This calculator's frequency selector shows how much the difference amounts to.
  • Fees compound too. A 1% annual fee at a 7% gross return is the same math run at 6%: on the worked example above it removes roughly $60,000 of the final balance. Run both rates and look at the gap before shrugging at an expense ratio.
  • Model in real dollars for planning. Subtract expected inflation from your return and rerun. The answer then reads in today's purchasing power, which is what you'll live on.
  • Steady beats spectacular. The formula assumes a constant return. Real markets lurch. The long-run average is what compounds, and the biggest threat to it is interrupting contributions when the chart dips.

Frequently asked questions

How much difference does compounding frequency make?

Less than most people expect. At 7 percent, $10,000 for 30 years grows to about $76,123 compounded annually and $81,165 compounded monthly, a real but modest gap. The rate and the time drive the result far more than frequency does. Frequency does make a difference when comparing quoted rates, so compare APY (which includes compounding) rather than nominal APR.

What return should I assume?

That depends on what the money is in, and no calculator can know the future. As reference points: US large-cap stocks have averaged roughly 10 percent annually over the past century before inflation, intermediate bonds closer to 5, and savings accounts track prevailing short-term rates. Many planners model diversified portfolios at 6 to 8 percent nominal. Run this calculator at a couple of rates to see the range.

Does this account for inflation?

Not unless you make it. Results are nominal: future dollars, which will buy less than today's. The clean trick is to enter a real (inflation-adjusted) return instead: if you expect 7 percent growth and 3 percent inflation, run the calculator at 4 percent and the answer comes out in today's purchasing power.

What is the Rule of 72?

A mental shortcut for doubling time: divide 72 by the annual return percentage to get the approximate years to double. At 7 percent, money doubles about every 10.3 years, so 30 years is roughly three doublings, turning $10,000 into about $80,000. The rule is an approximation of the exact logarithmic math this calculator does, accurate within a few percent for rates between 4 and 12.

Sources

  1. Compound Interest Calculator. Investor.gov, U.S. Securities and Exchange Commission. investor.govThe independent implementation of the same lump-sum-plus-deposits arithmetic that the formula section names as a place to check any result here.
  2. Appendix A to Part 1030 — Annual Percentage Yield Calculation (Regulation DD, Truth in Savings Act). Consumer Financial Protection Bureau. consumerfinance.govThe regulatory definition of APY, and the reason the FAQ and tips tell you to compare accounts on APY.
  3. How Fees and Expenses Affect Your Investment Portfolio — Investor Bulletin. U.S. Securities and Exchange Commission, 2025. investor.govThe SEC worked illustration of a 1% annual fee compounding against a portfolio, behind the tip that fees compound too.
  4. Returns on Stocks, Bonds and Bills: 1928-2024 — Historical Returns for the US. annual dataset maintained by Aswath Damodaran, NYU Stern School of Business. pages.stern.nyu.eduThe long-run US large-cap stock and Treasury-bond returns quoted in the FAQ on what rate to assume.

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