Future Value Calculator

A future value calculator answers one question: if a single sum earns a fixed annual rate and the growth stays invested, what will it be worth after a set number of years? This one takes three inputs (present value, annual rate and years) and applies the compound growth formula FV = PV × (1 + r)^t, with interest added once a year. The result is exact for that assumption. How useful it is depends on whether your money actually grows that way.

What each input means

Present value (PV) is the amount you have today, or the amount you would invest today. It is a single lump sum. The calculator does not take a series of deposits.

Annual rate (r) is the yearly growth rate as a percentage. The formula uses it as a decimal, so 6% becomes 0.06. For a savings account or certificate with a stated rate, enter that rate. For stocks or funds, the number you enter is an assumption, not a known figure. A negative rate is valid and models a constant yearly loss.

Years (t) is how long the money stays invested. Each year, the rate is applied to the full balance, including growth from earlier years.

What the two outputs tell you

Future value is the projected ending balance in dollars.

Growth is the total percentage gain over the whole period. It equals (1 + r)^t − 1, so it depends only on the rate and the number of years, not on the starting amount. At 6% over 10 years, growth is 79.08%. That figure holds whether you start with $500 or $5 million: each dollar becomes about $1.79. The growth figure is also much larger than 6% × 10 = 60%, and the 19-point difference is the effect of compounding.

The future value formula, variable by variable

FV = PV × (1 + r)^t

• FV: future value, the amount at the end
• PV: present value, the amount at the start
• r: interest or growth rate per period, as a decimal
• t (often written n): number of periods

The term (1 + r)^t is the future value factor. It shows what $1 grows to. Multiply it by any present value to get that amount’s future value. At 6% for 10 years the factor is about 1.7908.

The formula assumes the rate and the period match. Here both are annual: an annual rate applied once per year for a number of years.

Simple interest vs. compound interest

With simple interest, the rate applies only to the original principal:

FV = PV × (1 + r × t)

With compound interest, the rate applies to the whole balance each period, which is what this calculator does.

Take $1,000 at 10% for five years:

• Simple: $1,000 × (1 + 0.10 × 5) = $1,500. Every year adds the same $100.
• Compound: $1,000 × (1.10)^5 = $1,610.51. Year one adds $100. Year two adds $110, because 10% now applies to $1,100. Each later year adds more than the one before.

Negative rates

A negative rate shows what happens if value falls by the same percentage every year. $1,000 losing 5% a year for two years becomes $1,000 × (0.95)^2 = $902.50. That is a total decline of 9.75%, slightly less than 10%, because the second year’s loss applies to a smaller balance.

The same math covers declining-balance depreciation. A hypothetical $30,000 car that loses 15% of its value each year would be worth $30,000 × (0.85)^5 ≈ $13,311 after five years. Real depreciation is rarely that steady, but the formula gives a constant-rate estimate.

How to use the result

Test a goal

Enter what you have, a rate you consider realistic, and your time horizon. If the future value falls short of your target, you can change one of the three inputs: start with more, accept a different rate assumption, or wait longer.

Rearrange the formula for the missing variable

The same equation can be solved for any one variable when the other three are known:

• Present value needed: PV = FV ÷ (1 + r)^t
• Rate needed: r = (FV ÷ PV)^(1/t) − 1
• Time needed: t = ln(FV ÷ PV) ÷ ln(1 + r)

Example: to double money at 6%, t = ln(2) ÷ ln(1.06) ≈ 11.9 years. The Rule of 72 gives a quick approximation: 72 ÷ 6 = 12 years. The rule works best at moderate rates.

Example: $100,000 at a 10% annual return for 3 years is $100,000 × 1.331 = $133,100.

Compare options on the same terms

Running two options through the formula with the same horizon shows which one ends higher under each set of assumptions. Ending value alone can mislead, though. An option that requires $5,000 up front and another that requires $3,000 are not equivalent even if their ending values are close. Compare growth percentages, or the gain relative to what you put in, as well as dollar results.

Reverse it: present value

Present value runs the formula backward. It asks what a future amount is worth today at a given rate. At 5% for one year, $1,000 grows to $1,050, and $1,050 one year from now has a present value of $1,050 ÷ 1.05 = $1,000. The two concepts use the same rate, the same number of periods and the same factor. One multiplies by the factor and the other divides by it. Present value is the basis for pricing bonds and discounting future cash flows. Future value is the planning direction: today’s money projected forward.

What the calculator leaves out

The calculator’s formula covers one lump sum, one fixed annual rate and annual compounding. Each item below is outside that model, and each one can move the answer noticeably.

Regular contributions

If you add money every month or year, a lump-sum formula undercounts the ending balance. Recurring equal payments are an annuity, and their future value (payments at the end of each period) is:

FV = PMT × [(1 + r)^n − 1] ÷ r

Here PMT is the payment per period, r is the rate per period and n is the number of payments. For monthly deposits, use the monthly rate (annual rate ÷ 12) and the number of months.

Hypothetical example: $200 a month for 10 years at 6% a year, compounded monthly. The monthly rate is 0.005 and n is 120:

FV = $200 × [(1.005)^120 − 1] ÷ 0.005 ≈ $32,776

If deposits arrive at the start of each month (an annuity due), multiply by (1 + r): about $32,940. To project a starting balance plus ongoing contributions, run the lump sum through the calculator, calculate the annuity part separately, and add the two results.

Compounding more often than once a year

Many savings products compound daily or monthly. The general formula is:

FV = PV × (1 + r/m)^(m × t)

where m is the number of compounding periods per year. At 6% for 10 years, $10,000 compounded annually reaches $17,908.48. Compounded monthly, it reaches about $18,194. If a bank quotes an APY, that figure already reflects its compounding. Entering the APY as the annual rate in an annual-compounding formula gives a consistent result. Entering the nominal rate (APR) instead would understate growth slightly.

Inflation

The calculator’s output is in nominal dollars, meaning future dollars that may buy less than today’s. To express the result in today’s purchasing power, either discount the future value by inflation or use a real rate:

• Discount: real FV = nominal FV ÷ (1 + inflation)^t
• Real rate: (1 + nominal rate) ÷ (1 + inflation) − 1, then enter that rate

Hypothetical example: $17,908 after 10 years at 6%, with inflation assumed at 3% a year, is worth about $17,908 ÷ 1.3439 ≈ $13,326 in today’s dollars. The quick shortcut of subtracting inflation from the rate (6% − 3% = 3%) gives a close but slightly lower figure. Historical U.S. inflation rates by year show how much that assumption has varied over time.

Variable returns

The formula applies one rate every year. Market returns arrive unevenly, and the order matters. A gain of 20% followed by a loss of 20% leaves you at 1.20 × 0.80 = 0.96, a 4% loss, even though the simple average return is 0%. If you enter a long-run average from a volatile asset, you get the path where that exact rate happens every year. Actual results can land well above or below it.

Taxes, fees and withdrawals

Fund expenses, account fees and taxes on interest or gains all reduce the rate that actually compounds. A rough adjustment is to enter the rate net of annual fees. Withdrawals during the period break the single-lump-sum assumption entirely.

Sensitivity to the rate

Because the rate sits inside an exponent, small changes compound into large ones over long periods. Over 30 years, $10,000 at 6% grows to about $57,435. At 7% it grows to about $76,123. A single percentage point produces a difference of more than $18,000. Running the calculator at a low, middle and high rate gives a range, which is more useful than one figure that looks precise.

FAQ