Compound interest calculator

How does compound interest work?

Interest is added to the balance and then earns interest itself. $10,000 at 5% a year grows to $16,288.95 in 10 years compounded yearly — $6,288.95 of interest, against $5,000 with simple interest.

Does compounding more often help?

A little: the same $10,000 at 5% compounded monthly grows to $16,470.09 in 10 years, $181 more than yearly compounding.

How much do monthly contributions add up to?

$500 a month for 30 years at 6% compounded monthly grows to $502,257.52 — $180,000 you put in and $322,257.52 of interest.

What is the rule of 72?

A quick estimate of how long money takes to double: 72 ÷ the rate. At 6% that is about 12 years. The calculator gives the exact figure.

Are returns guaranteed?

No — the calculator assumes a steady rate. Savings accounts and CDs pay a stated rate; investments go up and down, and past returns do not promise future ones.

What is the difference between the interest rate and the APY?

The stated rate is the yearly rate before compounding; the APY (annual percentage yield) is what the balance really grows by in a year once compounding is counted. A 5% rate compounded monthly has an APY of 5.116%, and compounded daily 5.127%. Compare savings accounts and CDs by APY, not by the stated rate.

Why does starting ten years earlier matter so much?

Because the oldest deposits have the longest to earn interest on interest. $300 a month at 6% compounded monthly grows to $138,612 in 20 years but $301,355 in 30 years: ten more years adds $36,000 of deposits but $162,742 to the balance.

Does the calculator include taxes, fees or inflation?

No. The result is a nominal, pre-tax balance. Taxes on interest, account or fund fees and rising prices all reduce what the money can buy, so treat the figure as an upper bound on a steady rate. The inflation calculator and the real return calculator show the effect of prices.

The formula and what it assumes

Without deposits the balance is A = P × (1 + r ÷ n)^(n × t), where P is the starting amount, r the yearly rate as a decimal, n the number of compounding periods a year and t the years. The Securities and Exchange Commission’s investor education site describes compound interest as interest earned on both the original principal and the interest already added. This calculator also takes a monthly deposit. It converts the stated rate to the equivalent monthly rate, (1 + r ÷ n)^(n ÷ 12) − 1, then adds the interest and the deposit month by month, with each deposit made at the end of the month. The rate is assumed to stay constant for the whole period.

Worked example: $10,000 plus $200 a month for 10 years

At 5% compounded monthly with the deposit at the end of each month, the balance after 10 years is $47,526.55. You put in $10,000 + 120 × $200 = $34,000, so $13,526.55 is interest. The starting $10,000 alone, with no deposits, would reach $16,470.09; the deposits account for the rest. If the same lump sum were compounded only once a year, it would reach $16,288.95 instead of $16,470.09, a gap of $181.15.

Common mistakes

Entering the APY where the stated rate is expected counts the compounding twice and overstates growth slightly. Mixing up the deposit timing is another: deposits at the start of each month earn one more month of interest than the end-of-month deposits assumed here, so a bank statement can differ a little. A rate that is really an average of volatile yearly returns is not the same as a steady rate, because the order of good and bad years changes the result when deposits are made along the way. Last, a long horizon multiplies small errors in the rate: a one-point change in the rate moves a 30-year balance far more than a one-point change on a 3-year balance.

Estimates for planning only — not financial, tax or legal advice. Your lender's or employer's figures decide. How we check our calculators.

Sources: formula and definition of compound interest — U.S. SEC Office of Investor Education, Investor.gov “Compound Interest Calculator” and glossary; APY relationship — Truth in Savings Regulation (Regulation DD, 12 CFR part 1030), which requires banks to quote APY. Related: simple interest calculator, rule of 72 calculator, APY calculator, savings goal calculator and inflation calculator.