Future Value Calculator
✦ Finance & MoneyUse this free future value calculator to find what a lump sum or series of payments grows to — with any compounding frequency, annuity due or ordinary timing, and a period-by-period accumulation schedule.
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The formula
Future value — four modes
Lump sum: FV = PV x (1 + r/n)^(nxt)
Ordinary annuity: FV = PMT x [((1 + r/n)^(nxt) - 1) / (r/n)]
Annuity due: FV_due = FV_ordinary x (1 + r/n)
Growing annuity: FV = PMT₁ x ((1+r)^n - (1+g)^n) / (r - g) (r ≠ g)
FV = PMT₁ x n x (1+r)^(n-1) (r = g)
Continuous: FV = PV x e^(r x t)PV = present value (starting amount), PMT = payment per period, PMT₁ = first growing-annuity payment, r = periodic rate (annual rate / n), n = compounding periods per year, t = years, g = constant growth rate of payments per period. The combined case adds the lump-sum term and the annuity term. r = g is handled as a special case (FV = PMT₁ x n x (1+r)^(n-1)) to avoid division by zero. Continuous compounding uses the annual rate in e^(r x t). Full precision internally; rounded to 2 decimal places for display.
Calculating it by hand
- Choose your mode: single lump sum, equal payments (ordinary or annuity due), or growing payments.
- Enter the present value (PV) — the amount you invest or deposit today. In the payment modes a blank starting amount counts as 0; in lump-sum mode it is required.
- Enter the annual nominal rate (i) and the compounding frequency. The calculator divides i by n to get the periodic rate r.
- Set the time horizon in years. The total number of periods is n x t.
- For annuity modes, enter the payment per period (PMT) and choose ordinary (end-of-period) or annuity due (beginning-of-period) timing.
- The future value is FV = PV x (1+r)^(nxt) for a lump sum, plus PMT x [(GF-1)/r] for an ordinary annuity (where GF is the growth factor). Subtract total paid-in to find the interest earned.
Worked examples
$10,000 at 7% for 10 years, monthly compounding — lump sum
Periodic rate: r = 0.07 / 12 = 0.005833Total periods: n × t = 12 × 10 = 120Growth factor: (1.005833)^120 = 2.009661FV = $10,000 × 2.009661 = $20,096.61Interest earned: $20,096.61 − $10,000 = $10,096.61
Future value: $20,096.61. Interest earned: $10,096.61 — the money more than doubles in 10 years at 7% compounded monthly.
$500 per month for 10 years at 7%, ordinary annuity (end of period)
r = 0.07 / 12 = 0.005833; n = 120 periodsGrowth factor GF = (1.005833)^120 = 2.009661FV = $500 × [(2.009661 − 1) / 0.005833] = $500 × 173.0848 = $86,542.40Total paid in: $500 × 120 = $60,000Interest earned: $86,542.40 − $60,000 = $26,542.40
Future value (ordinary annuity): $86,542.40. Interest earned: $26,542.40 — 30.7% of the ending balance is growth from compounding.
$500 first payment growing 3% a year for 10 years at 7% — growing annuity (annual)
r = 7% a year = 0.07; g = 3% = 0.03; n = 10 annual periods(1 + r)^n = (1.07)^10 = 1.967151(1 + g)^n = (1.03)^10 = 1.343916FV = $500 × (1.967151 − 1.343916) / (0.07 − 0.03) = $500 × 15.58087 = $7,790.44Total paid in: $500 × (1.03^10 − 1) / 0.03 = $5,731.94; interest earned $2,058.50
Future value (growing annuity): $7,790.44. Each year's payment is 3% higher than the last — together the growing payments earn more than a flat $500 a year over the same horizon.
Methodology
How the future value formula works
Most people know the formula exists. What trips them up is the choice between ordinary annuity and annuity due — a single period of timing that can change the final figure by thousands of dollars on a long-horizon projection.
Read sources and limitsHow does the future value formula FV = PV × (1 + r)^n work?
Future value is compound interest in its simplest form: multiply a starting amount by (1 + periodic rate) once per compounding period, for every period in the horizon. Ten years compounded monthly is 120 periods. Growth is exponential, not linear, because each period's interest itself earns interest in every later period.
The growth factor (1 + r/n)^(n×t) sums up the whole compounding effect in one multiplier. At 7% compounded monthly for 10 years it is (1 + 0.07/12)^120 = 2.009661, so every dollar invested today grows to just over two dollars with no further deposits; $10,000 becomes $20,096.61.
Compounding frequency matters less than the rate. At 7%, monthly instead of annual compounding raises the effective annual yield from 7.000% to 7.229%, a gain of 0.229 points; raising the rate to 8% compounded monthly lifts it to 8.300%, a gain of 1.07 points.
What is the difference between an ordinary annuity and an annuity due?
With regular payments, timing decides how long each payment compounds. An ordinary annuity makes each payment at the end of its period, so the first one compounds for n − 1 periods. An annuity due makes it at the beginning, so the first one compounds for all n periods — one extra period of growth on every payment.
The annuity-due result is simply FV_ordinary × (1 + r). At 7% over 10 years with $500 a month, an ordinary annuity grows to $86,542.40 and an annuity due to $87,047.23 — $504.83 more, from one extra month of compounding on each payment. Over 30 years at a higher rate the gap widens.
Which to use depends on what you are modelling. Payroll contributions usually arrive at the end of the pay period (ordinary annuity); rent, leases and some saving plans pay at the start (annuity due). Most textbook examples default to ordinary; this calculator lets you toggle to match your real payments.
How does compounding frequency affect future value?
A 7% nominal rate means different things depending on how often interest is credited. Compounded annually, the effective annual yield is 7%; quarterly, (1 + 0.07/4)^4 − 1 = 7.186%; monthly, 7.229%; daily, 7.250%; and continuously, e^0.07 − 1 = 7.251%, the theoretical ceiling. Regulation DD defines the annual percentage yield banks quote the same way.
On $10,000 over 10 years at 7%, annual compounding gives $19,671.51, monthly $20,096.61 and continuous $20,137.53: monthly adds $425.10 over annual, and continuous only $40.91 more. A one-point change in the rate moves far more — 8% compounded monthly reaches $22,196.40, $2,099.79 above 7%.
So when comparing accounts, compare the effective annual yield, which already includes the compounding schedule. This calculator shows the periodic rate and the growth factor beside each result so you can check the convention being applied.
What is the difference between future value, present value and NPV?
Future value and present value are the same calculation run in opposite directions. Future value multiplies a present amount by the growth factor; present value divides a future amount by it. With identical rate and period inputs they always agree: the present value of a future value is the starting amount. Use the Present Value Calculator to work backwards.
Net present value (NPV) goes a step further: it sums the present values of all expected cash flows and subtracts the cost of the investment, and a positive NPV means the investment earns more than the chosen discount rate. The internal rate of return (IRR) is the rate at which NPV is zero. This calculator takes the rate as an input and does not solve for it.
What does this future value calculator not model?
The annual rate is held constant for the whole projection. Real investment returns vary from year to year, and savings rates reprice when the Federal Reserve moves. For a sensitivity check, run the calculator two or three times with different rates and compare the range — a range of outcomes is more informative than a single number.
Results are before tax and fees. In a taxable account, interest and realised gains are generally taxed in the year they are received (IRS Publication 550), which leaves less to compound; a tax-sheltered account is the closest match to the gross figures shown. To approximate an after-tax result, reduce the rate by your marginal tax rate.
Contributions are the same every period except in growing-annuity mode. Irregular deposits and gaps are not modelled; the Compound Interest Calculator on this site includes a yearly contribution-increase field.
This calculator provides educational estimates based on the assumptions you enter. It is not investment, tax, legal or financial advice. Investing involves risk, including possible loss of principal; actual results will differ from these projections.
Future Value questions
What is future value?
Future value (FV) is what a sum of money, or a series of payments, will grow to by a given date at a known interest or growth rate and compounding schedule. It is the reverse of present value: instead of discounting a future amount back to today, you compound a present amount forward. $10,000 at 7% compounded monthly has a future value of $20,096.61 after 10 years.
What is the future value formula?
For a lump sum: FV = PV × (1 + r/n)^(n×t), where PV is the present value, r the annual rate as a decimal, n the compounding periods per year and t the years. For equal end-of-period payments: FV = PMT × [((1 + r/n)^(n×t) − 1) / (r/n)]. For an annuity due, multiply the ordinary annuity result by (1 + r/n).
How do you calculate future value step by step?
For a lump sum: (1) divide the annual rate by the compounding frequency to get the periodic rate; (2) raise (1 + periodic rate) to the total number of periods to get the growth factor; (3) multiply the starting amount by it. $10,000 at 7% for 10 years monthly: r = 0.07/12 = 0.005833; (1.005833)^120 = 2.009661; FV = $20,096.61.
What is the future value of an annuity?
It is the value at the end of the last period of a series of regular payments, each compounded forward from the date it was made: FV = PMT × [((1 + r)^n − 1) / r]. $500 a month at 7% for 10 years, compounded monthly, grows to $86,542.40 — $60,000 paid in and $26,542.40 of interest earned on those payments.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period; an annuity due pays at the beginning. Each annuity-due payment compounds for one extra period, so FV_due = FV_ordinary × (1 + r). $500 a month at 7% for 10 years grows to $86,542.40 as an ordinary annuity and $87,047.23 as an annuity due — $504.83 more.
How does compounding frequency affect future value?
More frequent compounding gives a higher future value from the same nominal rate, because interest is credited, and starts earning interest, sooner. At 7%, monthly compounding gives an effective annual yield of 7.229% against 7.000% annually. On $10,000 over 10 years, monthly compounding adds $425.10 over annual, and continuous compounding only $40.91 more than monthly. The rate matters far more than the frequency.
What is a growing annuity and when is the formula used?
A growing annuity is a series of payments that rises at a constant rate g each period: FV = PMT₁ × ((1 + r)^n − (1 + g)^n) / (r − g), where PMT₁ is the first payment. It models salary-linked contributions or rent with an annual escalation clause. When r equals g the formula divides by zero, so FV = PMT₁ × n × (1 + r)^(n − 1) is used instead; this calculator handles that case automatically.
How much will $10,000 be worth in 10 years?
It depends on the rate. Compounded annually, $10,000 grows to $16,288.95 at 5%, $19,671.51 at 7% and $25,937.42 at 10%; compounding monthly at 7% gives $20,096.61. None of these allow for inflation, taxes or fees. Use a rate that matches the account — a savings rate for cash, a long-run assumption for stocks.
What will $500 a month be worth in 20 years?
At 7% a year, compounded monthly with deposits at the end of each month, $500 a month grows to $260,463.33 after 20 years — $120,000 paid in and $140,463 of growth. Over 30 years it reaches $609,985.50: the last ten years add more than the first twenty. Depositing at the start of each month adds about 0.6%; at 5% instead of 7% the 20-year figure is $205,516.83.
What is the Rule of 72 and how accurate is it?
The Rule of 72 estimates how long money takes to double: divide 72 by the annual rate. At 8% that is 9 years, and the exact figure with annual compounding is 9.01 years (1.08^9 = 1.999). At 6% the rule says 12 years against 11.9 exactly; at 12% it says 6 against 6.1. It is accurate to within a few months between about 4% and 12%; use the full formula for precise figures.
Does future value account for inflation?
Not unless you build it in. A future value is a nominal figure — the dollars you will hold — and inflation reduces what they buy. Use a real rate, (1 + nominal) ÷ (1 + inflation) − 1: 7% growth with 3% inflation is 3.88% real. $10,000 for 20 years at 7% is $38,696.84 nominal but about $21,426 in today's dollars. Taxes on interest or gains are a further reduction.
How do I calculate future value in Excel?
Use =FV(rate, nper, pmt, [pv], [type]). For a lump sum, =FV(6%, 10, 0, -10000) returns $17,908.48, the value of $10,000 after 10 years at 6%. For monthly deposits, =FV(6%/12, 120, -200) returns $32,775.87 for $200 a month over 10 years. Enter money you pay in as negative, use the rate and number of periods per compounding interval, and set type to 1 for deposits at the start of each period.
Source notes
Method, sources & limitations
Every figure on this page comes from the formula above applied to the values you enter. Nothing is estimated from market data, and no result is a forecast. These are the sources behind the method and any fixed figures it uses:
- U.S. Securities and Exchange Commission (Investor.gov) — Compound interest calculator (methodology reference)
- CFPB — Regulation DD, Appendix A to Part 1030: Annual Percentage Yield calculation
- Board of Governors of the Federal Reserve System — Selected Interest Rates (H.15)
- IRS Publication 550 — Investment Income and Expenses
Educational information only. Results are estimates produced from the assumptions you enter, and are not financial, tax, legal or medical advice. Check anything that matters against a qualified professional and the cited sources.