Simple & Compound Interest Calculator (Free)

A compound interest calculator uses A = P(1 + r/n)^nt: the principal P grows by r/n each period, n times a year, for t years. For example, $10,000 at 5% compounded monthly for 10 years becomes 10,000 × (1 + 0.05/12)¹²⁰ ≈ $16,470.09. Simple interest on the same money gives only $15,000.

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How to use the compound interest calculator

1. Future value: enter the principal, rate, compounding, time and any regular deposit (choose how often and whether it lands at the start or end of each period). Add an inflation rate to see the result in today’s dollars.
2. Simple vs compound: see both balances side by side, with a bar for every compounding frequency.
3. Find the rate, Find the time and Find principal: give three of the four values (P, A, r, t) and the calculator solves for the fourth.
4. Open Show steps for the full working, and the year-by-year table for running totals.

Compound interest formula

A = P(1 + r/n)^nt, and the interest earned is A − P.

• P is the principal (starting amount).
• r is the yearly rate as a decimal (5% = 0.05).
• n is how many times interest compounds a year: 1 annually, 2 semiannually, 4 quarterly, 12 monthly, 365 daily.
• t is the time in years (18 months = 1.5).

With annual compounding the formula shrinks to A = P(1 + r)^t. With continuous compounding it becomes A = Pe^rt: $10,000 at 5% for 10 years gives 10,000 × e^0.5 ≈ $16,487.21.

Simple interest vs compound interest

Simple interest is paid on the original principal only: I = Prt. Compound interest is, as Investor.gov puts it, “the interest you earn on interest”, so each period starts from the updated balance. Simple interest adds the same amount every year; compound interest multiplies by the same factor every year.

Worked example. $500 at 4% for 2 years. Simple: 500 × 0.04 × 2 = $40, so $540. Compounded annually: 500 × 1.04² = $540.80. The extra $0.80 is 4% interest on the first year’s $20.

How the compounding frequency changes the result

$10,000 at 5% for 10 years:

More frequent compounding always helps, but the gain shrinks fast. The rate and the time matter far more.

Compound interest with regular deposits

Each deposit compounds from the day it goes in. For deposits at the end of each period, their future value is PMT × ((1 + i)^N − 1) ÷ i, where i is the rate per deposit period and N the number of deposits. Deposits at the start of each period earn one extra period of interest, so multiply by (1 + i).

Worked example. $10,000 plus $100 at the end of every month at 5% compounded monthly for 10 years. The principal grows to $16,470.09 and the 120 deposits to $15,528.23, a total of $31,998.32. You put in $22,000, so $9,998.32 is interest. Making the same deposits at the start of each month gives $32,063.02.

Solving for the rate, the time or the principal

• Rate: r = n × ((A ÷ P)^1/(nt) − 1). Doubling $10,000 to $20,000 in 10 years with monthly compounding needs about 6.9515% a year.
• Time: t = ln(A ÷ P) ÷ (n × ln(1 + r/n)). At 5% compounded monthly, $10,000 reaches $20,000 in about 13.89 years.
• Principal (present value): P = A ÷ (1 + r/n)^nt. To have $20,000 in 10 years at 5% compounded monthly, start with about $12,143.22.

The Rule of 72

Divide 72 by the yearly rate in percent to estimate how many years money takes to double. Investor.gov gives the example of 9%: 72 ÷ 9 = 8 years. The exact doubling time with annual compounding is ln 2 ÷ ln(1 + r):

Inflation-adjusted value

Inflation is a general rise in prices, so a future dollar buys less. To express a future balance in today’s dollars, divide by (1 + inflation)^t. At an assumed 3% a year, the $31,998.32 above is worth about $31,998.32 ÷ 1.03¹⁰ ≈ $23,809.76 in today’s money. The calculator leaves the inflation rate to you; the BLS Consumer Price Index is the usual measure of past US inflation.

Common compound interest mistakes

• Using 5 instead of 0.05 for the rate.
• Dividing the rate by n but forgetting to multiply the exponent by n.
• Typing 1 + r/n^nt without parentheses, so only n is raised to the power. Write (1 + r/n)^(n*t).
• Rounding the growth factor early: keep at least 6 decimal places until the last step.
• Reporting A when the question asks for the interest, A − P.
• Mixing months and years: 18 months is t = 1.5.

Working compound interest by hand or in a spreadsheet

Without a calculator, multiply period by period: $200 at 10% compounded annually is 200 × 1.1 = 220 after one year and 220 × 1.1 = $242 after two. Before you start, estimate: the answer must be more than the simple interest result. With quarterly compounding, use the quarterly rate: $2,000 at 8% for one year is 2,000 × 1.02⁴ ≈ $2,164.86.

In Excel or Google Sheets, =1000*(1+0.05/12)^36 or =FV(0.05/12, 36, 0, -1000) both give $1,161.47 for $1,000 at 5% compounded monthly for 3 years. The FV function also handles deposits: put the deposit (as a negative number) in the third argument and 1 in the fifth for start-of-period timing.

Quick accuracy checklist for homework:

• Is the answer bigger than the simple interest answer (for a positive rate)?
• Does the exponent equal the total number of periods, n × t?
• Did you answer the question asked: the balance A or the interest A − P?
• Are money answers rounded to the cent only at the end?

Results are estimates for learning and planning, not financial advice. Savings rates change, and investment returns are not guaranteed.

Sources

Checked November 2026.

• Investor.gov (SEC), What is compound interest? (definition and Rule of 72)
• Investor.gov (SEC), Compound interest calculator
• CFPB, How does compound interest work?
• Investor.gov (SEC), What is risk? (inflation risk)
• U.S. Bureau of Labor Statistics, Consumer Price Index overview

Compound interest practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is the formula for compound interest?

A = P(1 + r/n)^nt, where P is the principal, r the yearly rate as a decimal, n the compounding periods per year and t the years. The interest is A − P.

Is compound interest calculated monthly or yearly?

It depends on the account. The rate is quoted per year, but interest can compound daily, monthly, quarterly or yearly. $1,000 at 6% for one year gives $1,060.00 compounded yearly and $1,061.68 compounded monthly.

How much will $10,000 be worth in 10 years with compound interest?

At 5% compounded monthly, about $16,470.09. At 5% compounded annually, $16,288.95. Change the rate in the calculator to see other cases.

How do you calculate compound interest with monthly contributions?

Grow the principal with P(1 + r/n)^nt, then add the future value of the deposits, PMT × ((1 + i)^N − 1) ÷ i. The Future value tab does both and shows each part.

How long does it take money to double?

Roughly 72 divided by the rate in percent: about 12 years at 6%. The calculator shows the exact doubling time next to the Rule of 72 estimate.

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