Compound Interest Calculator

How to use this compound interest calculator

1. Initial investment. The balance you start with today. Use 0 if you only plan to make monthly deposits.
2. Monthly deposit. The amount you add every month. It stays the same for the whole period.
3. Annual interest rate. The yearly rate before compounding, as quoted by a bank (often called APR or the nominal rate). For investments, enter the average yearly return you expect.
4. Compounding frequency. How often interest is added to your balance: from once a year up to continuously.
5. Years. How long the money stays invested, from 1 to 100 years.
6. Deposit timing. Whether each monthly deposit lands at the start or the end of the month. Start-of-month deposits earn a little more because they are invested one month longer.

Results update as you type. Use Copy link to this result to bookmark or share the exact scenario, and Download CSV to open the schedule in a spreadsheet.

What compound interest is

Compound interest means you earn interest on your original money and on the interest it has already earned. Each period, the interest is added to the balance, and the next period's interest is calculated on that larger balance.

Take $1,000 earning 5% a year, compounded once a year:

The interest grows every year even though the rate never changes. With simple interest you would earn a flat $50 each year and finish at $1,150. The gap is small at first and widens over time, which is why the time your money stays invested matters so much.

A handy shortcut is the rule of 72: divide 72 by the yearly rate to estimate how many years it takes to double your money. At 6% that gives 12 years; the exact answer with annual compounding is 11.9 years.

Worked examples

1. A steady monthly saver

Imagine you open an account with $5,000, add $250 at the end of every month, and earn 7% a year compounded monthly for 25 years.

• Total contributions$80,000.00
• Interest earned$151,145.01
• Final balance$231,145.01

More than half of the final balance (65.4%) is interest. Open this example in the calculator.

2. How much compounding frequency matters

Here is $10,000 left untouched for 15 years at a 6% nominal rate, compounded at different frequencies:

Going from annual to continuous compounding adds $630.45 over 15 years, and monthly versus daily is worth only $53.27. When comparing accounts, look at the effective annual yield (APY) rather than the compounding frequency on its own.

3. Depositing at the start of the month

Someone saving $400 a month for 30 years at 6.5%, compounded monthly, ends with $442,471.23 if each deposit is made at the end of the month and $444,867.95 if it is made at the start. Making each deposit at the start of the month instead of the end is worth $2,396.72 in this case, for exactly the same $144,000 of contributions.

4. Starting ten years earlier

Two savers each invest $300 a month at 7%, compounded monthly, and both stop counting 40 years from the first saver's start:

• Saver A: deposits for the first 10 years only, then leaves the money for 30 more years. Contributes $36,000$421,452.72
• Saver B: waits 10 years, then deposits for 30 years. Contributes $108,000$365,991.30

Saver A puts in a third as much money yet still finishes ahead. The early deposits had 30 extra years to compound.

Compound interest table

How $10,000 grows with monthly compounding and no further deposits, at common rates:

And what saving $100 a month from zero grows to, deposits at the end of each month:

At 7% a year, $10,000 roughly doubles every 10 years and reaches $81,165 after 30 years. Use the calculator above for any other combination.

Compound interest formula and how we calculate

For a single lump sum, the classic compound interest formula is:

A = P × (1 + r/n)^n×t

where P is the starting amount, r the nominal annual rate as a decimal, n the number of compounding periods per year and t the number of years. With continuous compounding it becomes A = P × e^r×t.

Because deposits here are monthly while interest can compound at a different frequency, the calculator first converts the nominal rate into the equivalent effective monthly rate:

i = (1 + r/n)^n/12 − 1   or, for continuous compounding,   i = e^r/12 − 1

It then steps through every month: a start-of-month deposit is added before that month's interest, an end-of-month deposit after it. The result is identical to the closed-form future value:

FV = P(1 + i)^N + D × [((1 + i)^N − 1) / i] × (1 + i if deposits are at the start of the month)

with N = 12 × years and D the monthly deposit. When the rate is 0 the result is simply P + D × N.

This approach keeps the effective annual yield exactly right for every frequency. One consequence: with annual compounding and monthly deposits, deposits made part-way through a year earn a proportional share of that year's interest. Some banks instead pay no interest on money deposited between crediting dates, which gives a slightly lower figure.

How we check it. The month-by-month schedule is tested against the closed-form formula for every compounding frequency and both deposit timings, against textbook values (for example $10,000 at 5% for 10 years compounded monthly is $16,470.09), and against edge cases such as a 0% rate, a single year and the 100-year maximum. Numbers are kept at full precision and rounded only for display, so rows in the schedule may differ from a hand total by a cent.

Compound interest in Excel and Google Sheets

For monthly compounding with monthly deposits, the spreadsheet FV function gives the same answer as this calculator. Enter the deposit and starting amount as negative numbers (money paid in):

=FV(rate/12, years*12, -monthly_deposit, -initial_investment, type)

Use type 0 for deposits at the end of each month and 1 for the start. For the calculator's default example, =FV(7%/12, 20*12, -200, -10000, 0) returns $144,572.72, the same figure the calculator shows for its default inputs.

For other compounding frequencies, first convert the rate to the effective monthly rate with =(1+rate/n)^(n/12)-1, where n is the number of compounding periods per year, and use that in place of rate/12.

APR, APY and compounding frequency

The annual percentage rate (APR), or nominal rate, is the headline yearly rate before compounding. The annual percentage yield (APY), also called the effective annual rate, is what you actually earn in a year once compounding is included. A 6% APR compounded monthly is an APY of 6.168%.

Savings accounts usually advertise APY, which already includes compounding. If you enter an APY in this calculator, choose Annually so the yield is not compounded a second time. Loans and some deposit accounts quote APR; enter that with its real compounding frequency. The Effective annual yield in the results shows the APY implied by whatever you enter.

To see a balance grow day by day, or to work with a daily percentage return, use the daily compound interest calculator.

What the result does not include

• Inflation. The result is in future money. Prices rise over time, so the same amount will buy less than it does today.
• Taxes. Interest and investment gains may be taxed each year or when you withdraw, depending on the account and where you live.
• Fees. Account, fund or advisory fees reduce the return. A 1% yearly fee on a 7% return leaves roughly 6%.
• Changing returns. The rate is fixed for the whole period. Real investment returns vary from year to year and can be negative.
• Changing deposits. Monthly deposits stay the same. Pay rises, breaks in saving or withdrawals are not modelled.

Saving toward a fixed amount? The savings goal calculator works backwards from your target to the monthly deposit you need.

Use the result to compare scenarios and set expectations, not as a promise of what an account will pay. Read our financial disclaimer for more.