Compound Interest Calculator

How the compound interest calculator works

Compound interest is interest earned on interest. Each period the interest is added to your balance, and the next period's interest is worked out on that larger balance, so the growth speeds up over time. Regular deposits feed the same snowball: every contribution starts earning interest of its own.

The calculator assumes a constant interest rate and a contribution paid at the end of each month. It converts the compounding frequency you choose (monthly, quarterly or annually) into the equivalent monthly rate, so the balance is right whatever the frequency. The table shows what you have put in, the interest earned in each year and the balance at the end of the year.

The compound interest formula

A = P × (1 + i)^12t + PMT × ((1 + i)^12t − 1) ÷ i
i = (1 + r ÷ n)^{n ÷ 12} − 1

• A: final balance
• P: initial deposit
• PMT: monthly contribution
• r: annual interest rate as a decimal (5% = 0.05)
• n: compounding periods per year (12 monthly, 4 quarterly, 1 annually)
• t: number of years
• i: equivalent monthly rate; with monthly compounding it is simply r ÷ 12

Without monthly contributions the formula reduces to the classic A = P × (1 + r ÷ n)^{n × t}.

Example: $10,000 plus $200 a month at 5%

Start with $10,000, add $200 a month and earn 5% compounded monthly: after 10 years the balance is $47,526.55. You have contributed $34,000, so $13,526.55 is interest. In the first year the interest is $567.39; in the tenth year it is $2,249.45, almost four times as much, because it is earned on a much bigger balance.

Monthly, quarterly or annual compounding

The more often interest is added, the faster the balance grows, but the effect is small. $10,000 left for 10 years at 5% with no further deposits grows to:

Monthly compounding adds only about $181 over annual compounding in ten years.

Time is the strongest lever

Saving $200 a month at 6% (compounded monthly) for 20 years gives $92,408.18 from $48,000 of deposits. Keep going for 30 years and the balance reaches $200,903.01 from $72,000 of deposits: ten more years add $24,000 of your money but $108,494.83 to the final balance. Saving twice as much, $400 a month, for only 15 years means the same $72,000 of deposits, yet it ends at $116,327.48, about $84,576 less than starting earlier with smaller amounts.

A handy shortcut is the rule of 72: divide 72 by the rate to estimate how many years it takes to double your money. At 6% that is 12 years, and $1,000 compounded annually at 6% does grow to $2,012.20 in 12 years.

APY, AER and the rate you enter

US banks quote savings rates as an APY (annual percentage yield) and UK banks as an AER (annual equivalent rate). Both already include the effect of compounding, so if you have one of them, choose annually and enter that figure. If instead you have a nominal rate paid monthly, choose monthly: 5% compounded monthly is the same as an APY of 5.12%. To find a good rate for your savings, see our comparison of the best free and high-yield savings accounts.

Tips to make compound interest work for you

• Start early and automate: a standing order on payday makes the monthly contribution happen without thinking about it.
• Mind the tax: interest and investment returns are often taxed unless they sit in a tax-advantaged account, such as an IRA or 401(k) in the US, an ISA in the UK or a TFSA in Canada. In Ireland deposit interest is subject to DIRT.
• Think in today's money: inflation erodes what the final balance can buy. To get a rough result in today's money, enter the rate minus the expected inflation rate.
• Remember that investment returns vary: a savings account pays a known rate, but stocks and funds go up and down from year to year. The calculator assumes a steady rate, so treat long-term results for investments as an illustration, not a promise.

How do I calculate compound interest?

Without regular deposits the formula is A = P × (1 + r/n)^(n × t): P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. With monthly contributions you add the future value of each deposit; this calculator does both for you and shows the balance year by year.

How much will $10,000 grow in 10 years at 5%?

With interest compounded annually, $10,000 at 5% becomes $16,288.95 after 10 years; compounded monthly it becomes $16,470.09. If you also add $200 every month, the balance reaches $47,526.55, of which $34,000 is your own money and $13,526.55 is interest.

What is the difference between simple and compound interest?

Simple interest is paid only on the original amount, while compound interest is also paid on the interest already earned. $10,000 at 5% for 10 years earns $5,000 of simple interest, but $6,288.95 of interest when it compounds once a year.

Does the compounding frequency make a big difference?

Less than most people think. $10,000 at 5% for 10 years grows to $16,288.95 with annual compounding, $16,436.19 with quarterly compounding and $16,470.09 with monthly compounding. The rate, the amount you save and above all the time you leave the money invested matter far more.

What is the rule of 72?

It is a quick way to estimate how long money takes to double: divide 72 by the annual rate. At 6% that gives 12 years, and indeed $1,000 compounded annually at 6% grows to $2,012.20 in 12 years. At 7.2% it doubles in about 10 years ($2,004.23).

Should I enter the APY or the interest rate?

If your bank quotes an APY (US) or AER (UK), choose annual compounding and enter that figure: APY and AER already include the effect of compounding. If you have a nominal rate with monthly compounding, choose monthly. A 5% rate compounded monthly is the same as a 5.12% APY.