Future Value Calculator

What future value means

Future value (FV) is what a sum of money will be worth at a later date if it earns a given rate of return. It is the forward-looking half of the time value of money: money you invest today grows, so an amount today is worth more than the same amount received later. Its mirror image is present value, which discounts a future amount back to today.

Future value is the number behind most savings goals. It answers questions such as how much a lump sum becomes after ten years, what a monthly deposit builds, or how much you would have left if you also take money out along the way. The same arithmetic, for a single deposit and without extra cash flows, is covered by the compound interest calculator.

How to use the calculator

• Initial value: the amount you start with. It cannot be zero.
• Number of periods: how long the money is invested, counted in years, half-years, quarters, months or days. It cannot be zero either.
• Interest rate: the nominal annual rate in percent. A rate of 0 is allowed.
• Compound frequency: how often interest is added to the balance, from annually to daily.
• Net cash flow (optional): a regular deposit, entered as a positive number, or a regular withdrawal, entered as a negative one, together with how often it happens.
• Cash flow occurs at: whether each deposit or withdrawal lands at the start or at the end of a compounding period. Money that goes in at the start earns one extra period of interest.

Deposits are pooled into one payment per compounding period. For example, $100 a month with annual compounding is treated as a single $1,200 payment each year. Days are counted at 365.2421 to the year.

The future value formula

Let P be the initial value, i the interest rate per compounding period (the annual rate divided by the number of compounding periods per year), N the number of whole compounding periods, and C the payment made each compounding period. A lump sum grows as:

FV = P × (1 + i)^N

Regular payments add the future value of an annuity. If they are made at the end of each period:

FV = P × (1 + i)^N + C × ((1 + i)^N − 1) ÷ i

If they are made at the start of each period, every payment earns one extra period of interest, so the annuity term is multiplied by (1 + i). When the rate is zero there is no growth at all and the formula collapses to FV = P + C × N.

Only whole compounding periods earn interest. If your term does not divide evenly, the leftover fraction of a period is ignored in the compounded balance. Seven months with semiannual compounding, for instance, earns one compounding period.

Worked example

You put $1,000 in an account that pays 5% a year, compounded annually, and add $100 at the end of every month for ten years. The monthly deposits add up to $1,200 a year, paid once per compounding period.

FV = 1,000 × 1.05¹⁰ + 1,200 × (1.05¹⁰ − 1) ÷ 0.05

The lump sum grows to 1,000 × 1.628895 = $1,628.89, and the deposits grow to 1,200 × 12.577893 = $15,093.47, so the future value is $16,722.37 (the two pieces are shown rounded; the unrounded sum is 16,722.3657). Here is how to read the rest of the output:

• Total cash flow is $12,000, the sum of the 120 monthly deposits.
• Interest accrued is $3,722.37: the future value minus the $1,000 start and the $12,000 deposited.
• Present value is $10,266.08, the future value divided by 1.05¹⁰. It is what the whole plan is worth in today's money at the same rate. The calculator discounts by (1 + i) raised to the number of years, with i the rate per compounding period: exact for annual compounding, a simplification for more frequent compounding.
• Effective interest rate is 5%, because annual compounding adds nothing beyond the stated rate.
• Capital growth is 1,572.237%, the future value divided by the initial value, minus one.

Timing matters too. With $1,000 at 4% compounded quarterly plus $200 every quarter for five years, deposits at the end of each quarter give $5,623.99, while deposits at the start give $5,668.03, because each one earns an extra quarter of interest.

How compounding frequency changes the answer

The more often interest is added, the more interest earns interest. The gap is modest, but it grows with time and with the rate. This table shows $10,000 invested for ten years at 6% a year, with no extra deposits:

Daily compounding adds only a little more again. The effective annual rate is the single yearly rate that would produce the same growth as the stated rate with its compounding: (1 + i)^{periods per year} − 1. It is the fairest number for comparing accounts that compound differently. A lump sum of $2,500 at 6% compounded monthly for eight years, for example, grows to $4,035.36.

Common mistakes

• Mixing up the units. A deposit of $100 per month and $100 per year differ by a factor of twelve. Check the dropdown next to the deposit.
• Forgetting withdrawals are negative. Enter money taken out as a negative number.
• Comparing nominal rates. Use the effective rate to compare accounts with different compounding.
• Ignoring inflation and tax. The result is in nominal dollars before tax and fees. Subtract expected inflation from the rate for a rough real-terms view.

Results are estimates that assume a constant rate, which real investments rarely deliver. This is not financial advice; see our disclaimer.