Compound Interest Calculator — growth at every compounding frequency

How it works

One formula: FV = P(1 + r/k)^(k·y). P is the starting amount, r the annual rate as a decimal, k the compounding periods per year (1 for annual through 365 for daily), y the years. Each period the balance earns r/k of itself, and the next period earns on the new, larger balance — the compounding. Interest earned is FV − P, and the growth multiple FV ÷ P says how many times over the money grew. The frequency table runs your exact inputs at every standard k so the usually surprising fact is visible in dollars: moving from annual to daily compounding changes the result by far less than one extra point of rate or one extra year of time.

Worked example

Both cases are LibreTexts' published examples. Invest $3,000 at 7% per year for four years, compounded annually: FV = 3000 × 1.07⁴ = $3,932.39. And the savings bond: $200 at 3.28% compounded semiannually for 30 years — k = 2, so FV = 200 × (1 + 0.0328/2)⁶⁰ = $530.77, the bond preset on this page. Every other number the page shows is the same formula at your inputs.

Frequently asked questions

What is compound interest?

Interest computed on the growing balance rather than only the original amount: each period's interest joins the principal, and the next period earns on both. Over short spans it looks like simple interest; over decades the curve bends upward — the bond example turns $200 into $530.77 without a single deposit.

How much does compounding frequency matter?

Less than most people expect, and the table proves it on your numbers: at ordinary rates, daily compounding beats annual by well under a tenth of the gain that one extra percentage point of rate delivers. Frequency is worth checking on an account, but rate and time are what compound wealth.

What does "compounded semiannually" mean?

The year is split into two periods and half the annual rate is applied each period — k = 2 in the formula. The bond example runs 60 half-year periods at 1.64% each, which is how 3.28% a year sustains thirty years of growth.

How long does money take to double?

Set the growth multiple to 2: solving the formula gives y = ln 2 ÷ (k·ln(1 + r/k)) — about 10 years at 7% compounded annually, which the default inputs nearly show. The rough "72 ÷ rate" mental shortcut approximates the same answer.

Does this include regular monthly deposits?

No — this page compounds a single starting amount. Recurring contributions are an annuity, a different formula that adds a payment stream to the compounding; that page is its own calculator in the savings family.

Is interest earned taxed?

Commonly, yes — interest in ordinary accounts is usually taxable income in the year earned, which lowers the effective rate, while tax-advantaged accounts defer or exempt it. This page computes the pre-tax arithmetic; the tax treatment belongs to your account type and jurisdiction.

How accurate is this, and what does it exclude?

The formula is exact for a constant rate and untouched principal. It excludes deposits and withdrawals, rate changes, fees, and taxes — and real accounts quote APY (which already bakes in compounding) versus a nominal rate, so check which your account states before entering it.