Free Compound Interest Calculator — Calculate Interest Rate Conversions

Compound Interest Calculator — Convert & Compare Interest Rates

Use this free compound interest calculator to convert interest rates between compounding frequencies — daily, bi-weekly, semi-monthly, monthly, quarterly, semi-annual, annual APR, annual APY, and continuous. See how a monthly APR compares to an annual APY, and compare products on an equal effective basis. For growth over time with contributions and schedules, use our Interest Calculator.

Compare APR and APY on the same basis — enter a rate and its compounding; the equivalent annual APY appears on the right.

Input

Interest rate (%)Compounding

Example: 6% with Monthly (APR) ≈ 6.16778% as Annually (APY). For growth over time with contributions, use the Interest Calculator.

Output

Shown as annually (APY).

Equivalent rate

—

How to use

Enter the interest rate as a percent (for example, 6 for 6%).
Choose how that rate is quoted on the left — for example, Monthly (APR) for a nominal annual rate compounded monthly.
Choose how you want the equivalent rate on the right — for example, Annually (APY) for the effective annual rate.
Click Calculate. Use Clear to reset to the default example.

How this compound interest calculator works

This tool converts an interest rate from one compounding convention to another by matching effective annual returns. Enter any rate and how it is quoted (for example, nominal APR compounded monthly), then choose how you want the equivalent rate expressed (for example, annual APY). Click Calculate to see the converted value. For balance growth over time with contributions, use the Interest Calculator.

Why it matters: A 6% rate compounded monthly is not the same as 6% compounded once per year. The monthly version corresponds to about 6.168% effective annually — a gap that grows with balance and time. Comparing products on the same basis avoids mixing APR and APY by mistake.

What is compound interest?

Compound interest is calculated on the original principal and on interest that has already been added to the balance. Simple interest, by contrast, applies only to the principal each period. Because each period's interest becomes part of the base for the next period, growth can accelerate over long horizons — the same mechanism helps investments grow and can make unpaid debt grow faster.

How compounding frequency affects returns

More frequent compounding means interest is credited more often, so there are more chances for interest to earn interest. At the same nominal annual rate, daily compounding slightly beats monthly, which beats quarterly, which beats annual. Differences in a single year are often small but compound into meaningful amounts over decades on large balances.

APR vs APY

APR (Annual Percentage Rate) here means the stated nominal annual rate for a given compounding schedule (for example, monthly). APY (Annual Percentage Yield) is the effective annual rate after compounding within the year — what you actually earn or owe per year at that quote and frequency. APY is always greater than or equal to the nominal APR when there is more than one compounding period per year.

Converting APR to APY uses APY = (1 + APR/n)^n − 1, where n is compounding periods per year. This calculator generalizes that idea across daily, bi-weekly, semi-monthly, monthly, quarterly, semi-annual, annual, and continuous conventions.

Compound interest formulas

Annual compounding: A_t = A₀(1 + r)ⁿ

Periodic compounding: A_t = A₀(1 + r/n)^nt with n periods per year.

Continuous compounding: A_t = A₀e^rt (Euler's number e ≈ 2.71828).

The Rule of 72

To estimate doubling time in years, divide 72 by the annual rate as a whole percent (use 8 for 8%, not 0.08). Example: 72 ÷ 8 ≈ 9 years. It is a rough guide; use exact compounding math or the Interest Calculator for precision.

Continuous compounding in practice

Continuous compounding is the mathematical limit as the number of periods per year grows without bound. Real accounts use discrete schedules (daily, monthly, and so on); continuous compounding is useful in theory and in advanced finance and is included here for completeness.

Frequently asked questions

APR vs APY, compounding frequency, the Rule of 72, and continuous compounding.

What is compound interest in simple terms?

Compound interest means you earn or owe interest on prior interest, not just on the original amount. Each period the balance that accrues interest grows, so growth can speed up over time on savings — or make debt harder to pay down if balances roll forward.

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the nominal annual rate for a stated compounding schedule. APY (Annual Percentage Yield) is the effective annual rate after compounding within the year. The same nominal APR compounded more often produces a higher APY. This calculator converts between those quotes.

How does compounding frequency affect interest?

More frequent compounding credits interest more often, so the effective annual rate rises if the nominal rate stays the same. Daily beats monthly beats quarterly beats annual in effective yield at a fixed nominal APR.

What is the Rule of 72?

A mental shortcut: years to double ≈ 72 ÷ (interest rate as a percent). At 6%, about 12 years. Best as a ballpark for moderate rates; use formulas or calculators for exact results.

Is compound interest good or bad?

It depends whether you are saving or borrowing. It accelerates wealth building on investments and can accelerate balance growth on high-interest debt if not paid down.

How do I calculate compound interest on a balance over time?

Use A = P(1 + r/n)^(nt) for discrete compounding, or our Interest Calculator for schedules, contributions, tax, and inflation. This page focuses on converting rates between compounding conventions, not projecting balances.

What is continuous compounding?

A theoretical limit where compounding happens at every instant: growth uses e^(rt). It is the upper bound for a given nominal rate; discrete daily compounding is very close in practice.

How much does compounding frequency matter in practice?

On typical savings balances, daily vs monthly is often a few dollars per year. On large loans or portfolios over many years, the difference between monthly and annual effective rates can be thousands of dollars.

Who uses this calculator

People comparing savings and CD quotes, borrowers comparing loan disclosures, students learning APR vs APY, investors checking whether a return is quoted as nominal or effective, and anyone who wants the same interest rate expressed under a different compounding schedule — without mixing incompatible metrics.