Future value calculator

What is future value?

What money today — and any regular payments — will grow to at a given rate. $1,000 at 6% a year for 10 years grows to $1,790.85.

What is the formula?

FV = PV × (1 + i)ⁿ + PMT × ((1 + i)ⁿ − 1) ÷ i, with i the rate per period and n the number of periods. Payments are at the end of each period.

How do regular payments add up?

$100 a month for 10 years at 6% compounded monthly grows to $16,387.93 — $12,000 paid in plus $4,387.93 of interest.

How long does it take money to double?

Roughly 72 ÷ the rate in years — about 12 years at 6%. At exactly 6% a year it is 11.9 years.

Does it include inflation?

No — it is in future dollars. Use the inflation calculator to see what that amount buys in today's money.

How much does compounding more often add?

Less than most people expect. $1,000 at 6% for 10 years becomes $1,790.85 compounded yearly, $1,814.02 quarterly and $1,819.40 monthly. The extra $28.55 from monthly compounding is under 2% of the final amount, because the effective yearly rate rises only from 6% to 6.17%.

What if my payments are made at the start of each period?

This calculator puts each payment at the end of the period, an ordinary annuity. A payment made at the start earns one extra period of interest, so the payment part of the result is multiplied by (1 + i). For $100 a month at 6% for 10 years, that lifts $16,387.93 to about $16,469.87.

How much do I need to save each month to reach a goal?

Work the formula backward for the payment. To reach $50,000 in 10 years at 6% compounded monthly from nothing, you would save about $305.10 a month.

How the calculation works

Money grows by a factor of (1 + i) each period, where i is the yearly rate divided by the number of periods in a year. After n periods, a starting amount PV has become PV × (1 + i)ⁿ. Each equal payment made at the end of a period grows for the periods that remain after it, and adding them up gives PMT × ((1 + i)ⁿ − 1) ÷ i. On this page the compounding period and the payment period are the same, so choosing monthly means you pay once a month.

Worked example: $1,000 today and $100 a month for 10 years

At 6% compounded monthly, i = 0.5% and n = 120. The $1,000 grows to $1,819.40, and the payments grow to $16,387.93, so the future value is $18,207.33. You paid in $13,000, so $5,207.33 is interest.

Common mistakes

Entering a yearly contribution while choosing monthly compounding is the most common slip, because the payment on this page is made once every compounding period. Entering a rate that already includes compounding, such as a bank’s APY, and then compounding it monthly is another; if you have an APY, choose yearly compounding. Treating the result as certain overlooks that the rate is assumed constant, which market returns are not. The figure is also in future dollars, before tax and fees, so it overstates what the money will buy.

Sources: the standard time-value-of-money formulas for a single sum and for equal payments (an ordinary annuity), as taught in OpenStax, Principles of Finance (Dahlquist and Knight), chapter 7, “Time Value of Money I: Single Payment Value,” and chapter 8, “Time Value of Money II: Equal Multiple Payments.” The yield on a deposit is defined in Regulation DD, 12 CFR Part 1030, Appendix A. Work backward with the present value calculator, plan a goal in the savings goal calculator, add a changing balance in the compound interest calculator or take out inflation with the inflation calculator.

Estimates for planning only — not financial advice. Your bank's disclosures decide. How we check our calculators.