Money
Future Value Calculator
Run the textbook future value formulas in three modes. Find the future value of a lump sum, the future value with periodic payments at the end or beginning of each period, or the time needed to grow a present value to a target. Each result shows the formula it used.
Mode
The amount today (PV). · e.g. 10,000
The nominal annual rate (r). · e.g. 7
The time horizon (t). · e.g. 10
Compounding frequency
FV after 10 years
$20,096.61
FV = PV × (1 + r/n)^(n × t)
A present value of $10,000.00 grows to $20,096.61 over 10 years at 7% (monthly compounding).
Examples
$10,000 at 7% for 10 yr, monthly
≈ $20,096 FV
$10,000 + $500/mo, 7%, 10 yr, monthly
≈ $106,608 FV
$10,000 → $50,000 at 7%, monthly
≈ 23 yr 1 mo
$1,000 at 7% for 20 yr, daily
≈ $4,055 FV
How it works
Future value (FV) is the amount that a present value (PV) grows to over time once interest is applied. The formulas below cover the three common variants, with one set of consistent variables: PV is the present value, PMT is the per-period payment, r is the nominal annual rate, n is compoundings per year, t is years, i is the effective per-period rate, and N is the number of payment periods.
Future value of a lump sum
FV = PV × (1 + r/n)^(n × t)
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)
Time to reach a future value
t = ln(FV / PV) / (n × ln(1 + r/n))
When payments and compounding occur at different frequencies, the calculator converts to a single period rate so the annuity and lump-sum pieces stay consistent: i = (1 + r/n)^(n/p) − 1 where p is payments per year.
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.
- 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.
- All money calculators.
Estimate, not financial advice. Future value is a nominal projection at the stated rate and compounding. Real returns, taxes, fees, and inflation change the actual result. For decisions that meaningfully affect your finances, talk with a qualified financial professional.
Frequently asked questions
Future value (FV) is what an amount today is worth at a later date once interest is applied. For a present value PV growing at an annual rate r for t years, the standard formula is FV = PV × (1 + r/n)^(n × t), where n is the number of compoundings per year. Continuous compounding uses FV = PV × e^(r × t).
For a lump sum: FV = PV × (1 + r/n)^(n × t). For an ordinary annuity (payments at end of period): FV = PMT × ((1 + i)^N − 1) / i. For an annuity due (payments at beginning of period): FV = PMT × ((1 + i)^N − 1) / i × (1 + i). When a lump sum and payments are combined, add the two future values.
Present value (PV) is the current worth of a future amount, discounted back at a given rate; future value (FV) is the future worth of a current amount, grown at a given rate. The two formulas are inverses of each other: PV = FV / (1 + r/n)^(n × t).
Timing. Ordinary annuity payments happen at the end of each period; annuity due payments happen at the beginning. Annuity due has one extra period of growth, so its future value equals the ordinary annuity future value times (1 + i). Pick whichever matches the cash flow you are modeling.
When payments occur on a different schedule than compounding, the calculator converts the annual rate into a single rate that applies to each payment period: i = (1 + annualRate / n)^(n / p) − 1, where n is compoundings per year and p is payments per year. Continuous compounding uses i = e^(annualRate / p) − 1. The same i is used for both the lump-sum growth and the annuity factor, so the two pieces stay consistent.
Use the target mode. Set the present value to any amount, the future value target to twice that amount, the rate, and the compounding. The Rule of 72 gives a quick estimate: time to double ≈ 72 / annual rate (in percent). At 6%, doubling takes about 12 years; at 9%, about 8 years. The calculator returns the exact time using logarithms.
Yes. Select Continuously in the compounding frequency picker. The math switches to e^(r × t) for a lump sum and e^(r / p) − 1 for the period rate when payments are involved. Continuous compounding is the theoretical limit and produces results slightly higher than daily compounding.
The lump sum future value equals the present value (no growth). For an annuity, the future value equals payment times the number of periods (linear). In target mode, a 0 rate means the present value cannot grow to a positive target, so the calculator flags that case rather than dividing by zero.
The savings calculator is goal-oriented and uses everyday savings language: how much should I save monthly, when will I reach my goal. The future value calculator is formula-oriented and matches the textbook finance setup: lump-sum future value, annuity future value with end- or beginning-of-period payments, and present-to-future-value time. Both produce consistent answers when the inputs match; pick the one whose framing matches your question.
No. The result is a nominal future value at the stated rate. To compare against today's purchasing power, subtract an inflation rate from the growth rate before running the calculator, or treat the rate as a real (inflation-adjusted) rate. The calculator also does not subtract income tax on interest.
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