Compound Interest Calculator

Compound interest means you earn interest on your interest. Each time interest is added to your balance, the next interest payment is calculated on a bigger amount. Over a few years the effect is small. Over a few decades it can be larger than all the money you put in yourself. This calculator shows how a starting amount and regular monthly deposits grow over time, year by year, with a chart and a table. You can compute compound interest in seconds, and the sections below explain the formula so you can also figure it out by hand.

How to use the calculator

• Enter your initial investment, the money you have now.
• Enter a monthly contribution. Use a negative number if you plan to take money out each month.
• Enter the number of years and your estimated yearly interest rate.
• If you are not sure about the rate, enter a variance range. For example, a rate of 6% with a range of 2 shows results for 4%, 6% and 8%.
• Choose how often interest is compounded, then press Calculate.

A simple example

You invest $1,000 today and add $100 every month for 5 years at 2% a year, compounded annually. At the end you have $7,348.93. You put in $7,000 yourself, so $348.93 is interest. The table shows the balance at the end of every year: $2,220.00 after year 1, $3,464.40 after year 2, and so on.

Why compounding frequency matters

Put $10,000 away at 7% for 30 years with no extra deposits. With annual compounding you end with $76,122.55. With monthly compounding you end with $81,164.97, and with daily compounding you end with $81,645.26. The rate is the same in each case. The only difference is how often interest is added to the balance. When you compare savings accounts, look at the APY (annual percentage yield), because it already includes the effect of compounding.

Time matters more than the rate

Two people each save $200 a month at 7%, compounded monthly, until age 65. The first person starts at 25 and saves for 40 years. They pay in $96,000 and end with about $524,963. The second person starts at 35 and saves for 30 years. They pay in $72,000 and end with about $243,994. The first person paid only $24,000 more, yet ends with more than twice as much money. The extra 10 years gave the interest more time to grow.

Withdrawals

You can enter a negative monthly amount to see how long your savings will last. For example, $100,000 at 4% with $1,000 taken out every month runs out during year 11. The calculator shows a warning in this case, and the balance stays at zero after that point.

Compound interest formula

For a single deposit, the compound interest formula is A = P × (1 + r/n)^(n × t). A is the final amount, P is the starting amount, r is the yearly rate as a decimal, n is the number of compounding periods per year and t is the number of years. When you also add money every month and interest is compounded monthly, the formula has a second part: A = P × (1 + i)^N + PMT × ((1 + i)^N − 1) / i. Here i = r/12 is the monthly rate, N = 12 × t is the number of months and PMT is the monthly contribution. For $1,000 plus $100 a month at 2% for 5 years, this gives $7,409.81. The calculator uses the same rules for every compounding option: deposits are added at the end of each month, and a deposit starts to earn interest at the next compounding date. This is the method the U.S. Securities and Exchange Commission uses in its calculator on Investor.gov, so the results match.

How to figure out compound interest by hand

When there is only one deposit, figuring out compound interest by hand takes five steps. As an example, take $5,000 at 6% a year, compounded quarterly, for 3 years:

• Divide the yearly rate by the number of periods per year: 0.06 ÷ 4 = 0.015.
• Multiply the periods per year by the number of years: 4 × 3 = 12 periods.
• Add 1 to the rate per period and raise it to the number of periods: 1.015^12 = 1.195618.
• Multiply the starting amount by this growth factor: $5,000 × 1.195618 = $5,978.09.
• Subtract the starting amount to find the interest: $5,978.09 − $5,000 = $978.09.

Accumulated interest formula

Accumulated interest is the part of your balance that came from interest. For a single deposit, the accumulated interest formula is I = P × ((1 + r/n)^(n × t) − 1). In the example above, $5,000 × (1.195618 − 1) = $978.09. When you also make contributions, use this formula: accumulated interest = final balance − (initial investment + all contributions). For $1,000 plus $100 a month for 5 years at 2% compounded annually, that is $7,348.93 − $7,000 = $348.93. The calculator shows this number as Interest earned, and the table shows how it builds up year by year.

Limits of this estimate

Real returns are not the same every year. Stock market returns go up and down, and savings account rates change. The calculator also ignores taxes, fees and inflation. Inflation is important over long periods: $81,000 in 30 years will buy much less than $81,000 buys today. Use the result as a guide, and run it again with a lower rate to see a careful case.