Future Value Calculator

What the future value calculator answers

The future value calculator runs the textbook future-value formulas for the three scenarios that show up most often in finance class and in real-world modeling:

• Lump sum: a single present value growing at a rate for a fixed time, with a choice of compounding frequency (annually, semi-annually, quarterly, monthly, daily, or continuously).
• With periodic payments: a present value plus equal periodic payments, with a separate payment frequency and a choice between end-of-period (ordinary annuity) and beginning-of-period (annuity due) timing.
• Present value to future value: the time it takes a present value to grow to a stated future value at a given rate.

How the future value calculator works

Pick a mode, enter the inputs, and the calculator:

• Applies the matching future-value formula for the chosen mode.
• Converts the annual rate and compounding frequency into a single period rate when payments occur on a different schedule than compounding.
• Distinguishes ordinary annuity (end of period) from annuity due (beginning of period) explicitly in the formula used.
• Reports the future value, total payments (when relevant), interest earned, period rate, period count, and the formula it ran.
• Flags the cases that have no finite answer (target cannot be reached with a 0 rate and no payments, present value already exceeds target, and so on).

Future value of a lump sum

The basic future value formula is FV = PV × (1 + r/n)^(n × t). The present value PV sits in an account earning a nominal annual rate r compounded n times per year for t years. Continuous compounding uses FV = PV × e^(r × t) and is the theoretical limit as n → ∞.

Example: $10,000 at 7% for 10 years with monthly compounding grows to about $20,096. The growth multiple is about 2.01×, so the lump sum roughly doubles in 10 years at 7% (a result the Rule of 72 also predicts: 72 / 7 ≈ 10.3 years to double).

Future value with periodic payments

When equal payments arrive each period, the future value is the future value of the present value plus the future value of the payment stream:

• Ordinary annuity (end of period): FV = PMT × ((1 + i)^N − 1) / i
• Annuity due (beginning of period): FV = PMT × ((1 + i)^N − 1) / i × (1 + i)

Annuity due has one extra period of compounding because every payment arrives one period earlier, which is why the formula adds a final × (1 + i) factor.

When payment frequency and compounding frequency differ, the calculator computes an effective rate per payment period using i = (1 + r/n)^(n/p) − 1 where n is compoundings per year and p is payments per year. The same i is then used for both the lump-sum growth and the annuity factor, which keeps the two pieces consistent.

Time to reach a future value

Inverting the lump-sum formula gives the time to grow from a present value to a stated future value: t = ln(FV / PV) / (n × ln(1 + r/n)) for discrete compounding, or t = ln(FV / PV) / r for continuous compounding. The Rule of 72 is a quick estimate for doubling time: 72 / annual rate (in percent) gives a close approximation.

At a 0% rate the present value never changes, so a positive target is unreachable; the calculator flags that case explicitly rather than dividing by zero.

Future value vs savings vs compound interest

All three calculators run the same underlying math but frame it differently:

• The future value calculator (this page) is the formula-first finance calculator. It exposes PV, PMT, r, n, t, and i directly and matches the textbook setup. Use it when the question is about applying or inverting a future-value formula.
• The savings calculator is goal-oriented. It uses everyday savings language and solves for future balance, monthly contribution, or time to goal. Use it when the question is about planning a savings goal, not running a formula.
• The compound interest calculator is a clean worked example of compounding itself. Use it to see how principal, rate, time, and frequency combine into a single growth example.

All three produce consistent answers when the inputs line up. Pick the one whose framing matches your question.

Worked examples

• Lump sum: $10,000 at 7% for 10 years with monthly compounding. FV ≈ $20,096, interest earned ≈ $10,096, growth multiple ≈ 2.01×.
• With payments: $10,000 plus $500 per month at 7% for 10 years (monthly compounding, end of period). FV ≈ $106,608, total payments $60,000, interest earned ≈ $36,512.
• Time to target: $10,000 to $50,000 at 7% with monthly compounding takes about 23 years 1 month (about 277 months). The Rule of 72 estimate for each doubling at 7% is roughly 10.3 years, and growing to 5× requires a bit more than two doublings.
• Daily compounding: $1,000 at 7% for 20 years with daily compounding grows to about $4,055, slightly higher than the $3,870 you would get with annual compounding at the same rate.

Common mistakes

• Mixing payment frequency and compounding frequency without converting to a single period rate. The calculator does this conversion automatically; doing it by hand requires i = (1 + r/n)^(n/p) − 1.
• Treating an annuity due like an ordinary annuity. Annuity due payments arrive one period earlier and pick up one extra period of compounding, so the future value is higher by a factor of (1 + i).
• Using a nominal rate where the formula expects an APY, or vice versa. The APY calculator converts between the two cleanly.
• Forgetting that future value is nominal. The calculator does not subtract inflation or income taxes.
• Trying to grow a 0 present value to a positive future value through compounding alone. Add a positive present value or use the with-payments mode.

Related tools

• Savings calculator for goal-oriented savings planning.
• Inflation calculator for purchasing-power decay (the mirror image of future value).
• Emergency fund calculator for a months-of-coverage cash goal.
• Compound interest calculator for a clean worked example of compounding.
• Simple interest calculator for non-compounding interest problems.
• APY calculator to convert nominal rates to APY.
• 401k calculator for retirement savings with employer match.
• Roth IRA calculator for after-tax retirement projections.
• Simple interest vs compound interest explains the two formulas and why long-horizon future value math is compound.
• Present value calculator for the inverse: what a future amount is worth today.
• NPV calculator for the present value of a series of future cash flows.
• IRA calculator for Traditional or Roth IRA growth with a year-by-year table.
• 529 calculator for tax-advantaged college savings projections.
• Coast FIRE calculator for the portfolio size that compounds to a target FIRE number.
• All money calculators.

One projection worked by hand

Take $10,000 at 6% a year, compounded monthly, for ten years. The periodic rate is 0.06 / 12 = 0.005 and there are 12 x 10 = 120 periods.

Keep the digits. Rounding the growth factor to 1.82 gives $18,200, which is $6.03 out on a ten-thousand-dollar balance and grows with the amount.

Simple interest on the same terms would give 10,000 x (1 + 0.06 x 10) = $16,000. The $2,193.97 difference is the whole of what compounding contributes over ten years.

What the number does not include

A future value is a model, and the honest part of the answer is the list of things it leaves out. This one deducts none of:

• Tax on interest or on gains, at any rate, in any year.
• Fees, whether an expense ratio inside a fund or a platform or advisory charge on top of it.
• Inflation. The answer is in future dollars.
• Withdrawals of any size at any point in the term.

Inflation is the one most often forgotten, because the figure looks like money you recognise. At 3% a year, $18,193.97 ten years out buys what $13,538 buys today: about 74% of the purchasing power the number appears to promise. Nothing has gone wrong with the arithmetic. The projection is nominal, and a nominal figure is not a real one.

If you want a real answer, put a real rate in. Subtract your inflation assumption from the growth rate before running the calculator and read the result as today's money.

Edge cases worth knowing

• A zero present value cannot grow into anything through compounding alone. Multiplying zero by any growth factor is still zero, which is why that mode asks for a payment stream instead.
• A zero rate makes the growth factor exactly 1, so the future value equals the present value plus any payments. That is correct rather than a failure.
• A negative rate is arithmetically fine and shrinks the balance. It is the right way to model a real return when inflation exceeds the nominal rate.
• Fractional years work, but the period count stops being a whole number, so the answer assumes growth accrues through the final partial period rather than landing on a compounding date.
• Very long terms magnify the rate assumption rather than the starting amount. Over forty years a single percentage point on the rate moves the answer more than doubling the present value does.

Your figures stay in your browser

Nothing you type leaves this page. The arithmetic runs in your browser, there is no account and no login, and no amount, rate or term is sent anywhere or stored.