Future Value Calculator

Apply the time value of money: FV = PV × (1 + r)ⁿ. See what a lump sum becomes after compounding.

How the Future Value Calculator works

This calculator solves one equation: FV = PV x (1 + r)ⁿ, the future value of a single lump sum. It answers a narrow question on purpose - what does one amount of money, deposited once and left untouched, become after growing for a set number of periods? No recurring deposits, no withdrawals, just one cash flow moved forward in time.

The variables, defined

• FV - future value, the ending dollar amount the tool returns.
• PV - present value, the single lump sum you put in today.
• r - the periodic growth rate as a decimal (6% per year = 0.06).
• n - the number of compounding periods (years, if r is annual).

What the calculator does step by step

1. Reads your lump sum (PV), rate, and number of periods.
2. Converts the rate to a decimal and, if you choose a non-annual frequency, splits it into a periodic rate (r/m) and scales the period count (n x m).
3. Computes the growth factor (1 + r)ⁿ - the multiplier your money grows by.
4. Multiplies PV by that factor to return FV.
5. Reports the total growth (FV - PV) so you see how much came from compounding versus your original deposit.

Edge cases it handles

When r = 0%, the factor (1 + 0)ⁿ equals 1, so FV simply equals PV - no division blows up because there is no division here (unlike present value, which divides). A negative rate models a declining asset, returning an FV below PV. Fractional periods (n = 7.5) are valid because exponentiation accepts decimals. For continuous growth the engine switches to FV = PV x e^rt, where e is about 2.71828. Because this is a single-cash-flow tool, the formula has no annuity term - if you plan to add money regularly, that is a different equation and a different calculator.

Example calculation

Three lump-sum scenarios, each with one deposit and no further contributions, recomputed with FV = PV x (1 + r)ⁿ.

Scenario 1: A windfall left to grow

You inherit $25,000 and park it in a diversified fund expecting 6% a year for 20 years, adding nothing more. FV = 25,000 x (1.06)²⁰ = 25,000 x 3.20714 = $80,178.39. Your single deposit more than tripled; $55,178.39 of the ending balance is pure growth.

Scenario 2: A small early gift

A relative gives a newborn $5,000 invested at 8% for 30 years. FV = 5,000 x (1.08)³⁰ = 5,000 x 10.06266 = $50,313.28. One $5,000 deposit becomes over $50,000 - a 10x multiple - purely because time and rate did the work.

Scenario 3: A conservative parking spot

You hold $100,000 in a steady 4% vehicle for 15 years. FV = 100,000 x (1.04)¹⁵ = 100,000 x 1.80094 = $180,094.35. Lower rate, shorter horizon, large principal - the balance still nearly doubles.

Side-by-side comparison

Scenario	Lump sum (PV)	Rate (r)	Years (n)	Growth factor	Future value (FV)	Total growth
Windfall	$25,000.00	6%	20	3.2071	$80,178.39	$55,178.39
Newborn gift	$5,000.00	8%	30	10.0627	$50,313.28	$45,313.28
Conservative hold	$100,000.00	4%	15	1.8009	$180,094.35	$80,094.35

The newborn gift shows why rate and time beat size: a $5,000 deposit at 8% for 30 years grows by 906%, while the $100,000 deposit at 4% for 15 years grows by only 80%. To see what that ending balance is worth in today's dollars, run the inverse on the present value calculator, or model adding monthly money on the compound interest calculator.

Tips for using the Future Value Calculator

• <strong>Use this tool only for a single deposit.</strong> The moment you plan to add money each month, the lump-sum formula understates your result - switch to the <a href="/investment-calculator/">investment calculator</a>, which adds a separate annuity term for the contributions.
• <strong>Match the rate to the period.</strong> If n is in months, r must be a monthly rate (annual / 12). Mixing an annual rate with a month count is the single most common error and inflates FV by orders of magnitude.
• <strong>Always deflate the answer for real planning.</strong> The FV is nominal. At 2.5% inflation, the $80,178 from a 20-year hold buys what about $48,931 buys today. Sanity-check every nominal FV against the <a href="/inflation-calculator/">inflation calculator</a> before celebrating.
• <strong>Use FV to compare lump-sum offers head-to-head.</strong> Offered $20,000 now or $30,000 in 8 years? Grow the $20,000 at your real opportunity rate: 20,000 x (1.07)⁸ = $34,364, which beats $30,000. Take the cash now.
• <strong>Reach for the Excel one-liner when you need a quick number.</strong> =FV(rate, nper, 0, -PV) returns the same answer. The pmt argument is 0 precisely because a lump sum has no recurring payment - that zero is what makes it a single-cash-flow calculation.
• <strong>Enter the deposit as a negative in Excel.</strong> =FV(0.06, 20, 0, -25000) returns a positive $80,178.39. A positive PV returns a negative FV because Excel treats cash you part with as an outflow.
• <strong>Pick continuous compounding only when the asset actually grows continuously.</strong> FV = PV x e^rt adds about 3.5% over annual compounding at 6% for 20 years ($83,003 vs $80,178). Use it for theoretical or bond-pricing work, not a savings account that credits monthly.
• <strong>Stress-test with a lower rate.</strong> Long-horizon FV is brutally sensitive to r. Re-run Scenario 1 at 5% instead of 6% and the ending balance drops from $80,178 to about $66,332 - a 17% haircut from one percentage point. Never plan on an optimistic single rate.
• <strong>Remember FV and present value are exact inverses.</strong> If FV = PV x (1 + r)ⁿ, then PV = FV / (1 + r)ⁿ. Computing one and discounting back should return your original number - a free accuracy check.
• <strong>Use FV before locking up cash.</strong> Before buying a multi-year CD or a fixed annuity, project the guaranteed FV and compare it to what the same lump sum might earn elsewhere. The gap is the price of certainty.

Future value of a lump sum vs future value of an annuity

A lump sum grows one deposit forward; an annuity grows a stream of equal deposits forward - and they use different formulas. This calculator handles only the lump sum, FV = PV x (1 + r)ⁿ. An annuity (regular monthly or annual payments) uses FV = PMT x [((1 + r)ⁿ - 1) / r], a separate term that sums the growth of each individual deposit.

The distinction matters when comparing equal total dollars. Suppose you can deposit $25,000 today as one lump, or $1,250 a year for 20 years (also $25,000 total). At 6%:

Approach	Formula	Total deposited	Future value at 6%, 20 yr
Lump sum today	PV x (1 + r)n	$25,000	$80,178.39
$1,250/year annuity	PMT x [((1 + r)n - 1) / r]	$25,000	$45,982.00

The lump sum wins by $34,196 even though the dollars deposited are identical, because every dollar of the lump sum compounds for the full 20 years, while the annuity's later deposits compound for only a year or two. That gap is the entire reason a single upfront deposit and a spread-out savings plan need separate calculators. If your money is recurring rather than upfront, model it on the compound interest calculator instead.

How to calculate future value by hand and in Excel

By hand: raise (1 + r) to the power n, then multiply by your lump sum. For $25,000 at 6% for 20 years: compute 1.06²⁰ = 3.20714, then 25,000 x 3.20714 = $80,178.39. Any calculator with a y^x or ^ key does the exponent in one keystroke.

In a spreadsheet, two routes give the same result:

• The FV function: =FV(rate, nper, pmt, pv). For a lump sum, set pmt to 0 and pv negative: =FV(0.06, 20, 0, -25000) returns $80,178.39. The zero pmt is what marks it as single-cash-flow; any nonzero pmt would turn it into an annuity calculation.
• The raw formula: =25000*(1.06)^20 returns the same number with no sign juggling.

To go the other direction and discount a future amount back to today, use =PV(rate, nper, 0, -fv) - the inverse function powering the present value calculator. Google Sheets uses the identical syntax for both.

Nominal vs real future value

Nominal future value ignores inflation; real future value strips it out to show true purchasing power. This calculator returns nominal dollars - the literal balance you will see on a statement. But a dollar in 20 years buys less than a dollar today, so the nominal figure overstates what your money can actually purchase.

There are two ways to find the real value. Deflate the nominal FV: $80,178.39 / (1.025)²⁰ = $48,930.54 in today's purchasing power at 2.5% inflation. Or use a real rate of return from the start: (1.06 / 1.025) - 1 = 3.415%, and 25,000 x (1.03415)²⁰ = the same $48,931. Both methods agree.

Scenario	Nominal FV	Real FV (2.5% inflation)
$25,000 at 6%, 20 yr	$80,178.39	$48,930.54
$5,000 at 8%, 30 yr	$50,313.28	$23,986.49
$100,000 at 4%, 15 yr	$180,094.35	$124,348.95

For long horizons the gap is enormous - the $5,000 gift's real value is less than half its nominal value after 30 years. Always pair an FV projection with the inflation calculator.

Discrete vs continuous compounding

Discrete compounding credits growth at fixed intervals; continuous compounding credits it every instant using FV = PV x e^rt. The standard formula FV = PV x (1 + r/m)^nm covers discrete cases - annual (m = 1), monthly (m = 12), daily (m = 365). As m approaches infinity, the expression converges to PV x e^rt, where e is about 2.71828.

The practical gap is small. For $25,000 at 6% over 20 years:

Compounding	Formula	Future value
Annual	25,000 x (1.06)20	$80,178.39
Monthly	25,000 x (1.005)240	$82,755.11
Continuous	25,000 x e(0.06 x 20)	$83,002.92

Going from annual to continuous adds only about 3.5% over 20 years. Continuous compounding shows up mainly in bond math, options pricing, and academic models; for a real bank product, the discrete frequency your account actually uses is the honest input. The effective annual rate of a 6% continuous rate is e^0.06 - 1 = 6.18%.

Using future value to compare lump-sum offers

To compare offers paid at different times, grow every amount to a common future date and pick the largest - or discount them all to today and pick the largest; both rank them identically. This is where a single-cash-flow FV calculator earns its keep: lawsuit settlements, buyout offers, lottery cash-vs-annuity choices, and deferred bonuses all become comparable.

Example: a buyer offers $20,000 today or $30,000 in 8 years. Your realistic opportunity rate is 7%. Grow the cash offer: 20,000 x (1.07)⁸ = $34,363.72. Because $34,364 beats the $30,000 deferred offer, taking the cash and investing it wins by about $4,364 in year-8 dollars. Flip the rate to 3% and the deferred offer would win instead - the decision hinges entirely on the rate you can actually earn.

The mirror-image method is to discount the future offer to today on the present value calculator: $30,000 in 8 years at 7% is worth $17,460 now, less than $20,000 - same conclusion. For comparing investment payouts more broadly, the ROI calculator adds a percentage-return lens.

Future value of a lump sum: $10,000-$100,000 at 4%, 6% and 8% over 20 years

A lump-sum future value is one deposit grown by FV = PV x (1 + r)ⁿ with no recurring contributions. The table below shows what a single deposit becomes after 20 years of annual compounding at three common return rates. Every figure is recomputed; for example $50,000 at 6% for 20 years is 50,000 x 1.06²⁰ = $160,357.

Lump sum (today)	At 4%	At 6%	At 8%
$10,000	$21,911	$32,071	$46,610
$25,000	$54,778	$80,178	$116,524
$50,000	$109,556	$160,357	$233,048
$100,000	$219,112	$320,714	$466,096

All results are nominal dollars before inflation; at 3% inflation over 20 years, divide by about 1.81 to see purchasing power in today's money. Notice the columns scale linearly with the deposit - doubling the lump sum doubles the FV - but jump sharply across rates, which is why the rate you assume matters more than the size of the deposit. Doubling roughly every 12 years at 6% and every 9 years at 8% matches the Rule of 72.

Common mistakes with future value calculations

Most future value errors come from mismatched units, the wrong rate, or forgetting inflation. The four that distort answers most:

• Mixing rate and period units. Pairing an annual 6% with a month count of 240 instead of 20 produces a wildly wrong number. If n is months, r must be monthly (0.06 / 12 = 0.005).
• Adding contributions in your head. This formula assumes one deposit and nothing more. If you mentally include monthly savings, your real result will far exceed the lump-sum FV - use a contribution calculator instead.
• Treating nominal FV as spendable wealth. An $80,000 nominal balance in 20 years feels like a lot, but inflation may cut its purchasing power by 40% or more. Always compute the real value too.
• Using an optimistic single rate. Long-horizon FV is hypersensitive to r. One extra percentage point over 30 years can change the answer by 30% or more, so plan with a conservative rate and treat upside as a bonus.

A final subtle one: confusing FV with present value. They are inverses - FV multiplies by (1 + r)ⁿ, PV divides by it. Plugging into the wrong one quietly doubles or halves your error.

Is your future value good? Reference benchmarks

A useful benchmark: a lump sum at a 7% long-run return roughly doubles every 10 years, so judge your FV against simple doubling milestones. The Rule of 72 gives the shortcut - 72 divided by your rate is the approximate doubling time. At 7%, that is about 10.3 years; at 9%, about 8 years; at 6%, about 12 years.

Here is how a single $10,000 lump sum stacks up at common rates, so you can see whether your own projection is reasonable:

Lump sum	Rate	10 years	20 years	30 years
$10,000	4%	$14,802	$21,911	$32,434
$10,000	7%	$19,672	$38,697	$76,123
$10,000	10%	$25,937	$67,275	$174,494

If a salesperson projects a lump sum tripling in 10 years, that implies roughly an 11.6% guaranteed annual return - far above what any safe product delivers, so treat it skeptically. For perspective, US large-cap stocks have averaged near 10% nominal over the very long run, but with large year-to-year swings. To turn a target FV into a plan, work backward with the savings goal calculator.

Related on this site

present value calculator · compound interest calculator · investment calculator · Rule of 72 calculator · inflation calculator · savings goal calculator

For a related deep dive, see SEC Investor.gov investing basics.

Future Value Calculator — frequently asked questions

What rate to use?

Use an expected return for investments or an interest rate for accounts.

Include contributions?

This is a single lump sum. Use the compound interest calculator for ongoing deposits.

What's the difference from compound interest?

Future value here is a single lump sum; the compound calculator adds recurring contributions.

Does inflation affect this?

These are nominal figures; subtract inflation for real purchasing power.

How much will a $25,000 lump sum grow to in 20 years at 6%?

A one-time $25,000 deposit grows to about <strong>$80,178</strong> in 20 years at 6% compounded annually. The math is FV = PV x (1 + r)ⁿ = 25,000 x 1.06²⁰ = $80,178.39. Only your original $25,000 works here, no new deposits, so the $55,178 gain is pure compounding. Try other figures in the <a href="/future-value-calculator/">future value calculator</a>.

How do I calculate future value of a lump sum in Excel?

Use <strong>=FV(rate, nper, pmt, pv)</strong> with pmt set to 0 for a lump sum. For $10,000 at 7% for 10 years, enter =FV(0.07,10,0,-10000), which returns <strong>$19,671.51</strong>. Enter pv as a negative number (cash leaving you) so the result shows positive. The 0 payment is what makes it a lump sum rather than an annuity. This matches FV = 10,000 x 1.07¹⁰.

What is the difference between future value of a lump sum and future value of an annuity?

A lump sum grows one deposit; an annuity grows a stream of equal payments. One $50,000 deposit at 6% for 10 years reaches <strong>$89,542</strong> (50,000 x 1.06¹⁰). But $5,000 paid yearly for 10 years at 6% reaches only <strong>$65,904</strong>, because the later payments compound for fewer years. Lump-sum FV uses (1 + r)ⁿ; annuity FV uses ((1 + r)ⁿ - 1) / r.

How do I calculate future value by hand without a calculator?

Multiply the principal by (1 + rate) once for every year. For $15,000 at 3% over 5 years, compute 1.03 x 1.03 x 1.03 x 1.03 x 1.03 = 1.159274, then 15,000 x 1.159274 = <strong>$17,389.11</strong>. That is FV = PV x (1 + r)ⁿ done step by step. For long terms this gets tedious, so the <a href="/future-value-calculator/">calculator</a> or Excel saves time.

What is the real (inflation-adjusted) future value of $30,000 in 20 years at 7%?

Nominally $30,000 at 7% for 20 years grows to <strong>$116,091</strong>, but in today's dollars at 3% inflation it is worth about <strong>$64,277</strong>. Divide nominal FV by (1.03)²⁰, or use the real rate (1.07 / 1.03 - 1 = 3.88%) directly: 30,000 x 1.0388²⁰ = $64,277. Real FV shows actual purchasing power, not just a bigger number. See the <a href="/inflation-calculator/">inflation calculator</a>.

What is continuous compounding future value and how does it differ from annual?

Continuous compounding uses FV = PV x e^rt and gives the mathematical maximum FV for a given rate. For $10,000 at 6% over 10 years, continuous gives <strong>$18,221.19</strong> versus annual compounding at <strong>$17,908.48</strong>, a gap of about $313. The difference exists because continuous compounding credits growth at every instant rather than once a year. Real accounts compound monthly or daily, landing between these two.

How much does compounding frequency change the future value of $10,000 at 6% over 10 years?

Frequency adds a few hundred dollars, not a fortune. At 6% for 10 years, $10,000 becomes <strong>$17,908</strong> annually, <strong>$18,061</strong> semiannually, <strong>$18,194</strong> monthly, and <strong>$18,220</strong> daily. The jump from annual to monthly is about $285; monthly to daily adds only $26. The rate and the time horizon matter far more than how often interest posts. The <a href="/apy-calculator/">APY calculator</a> converts frequency into one comparable yield.

Is leaving $1,000 invested for 40 years at 10% worth it?

Yes, time turns a tiny lump sum into real money. One $1,000 deposit at 10% for 40 years grows to about <strong>$45,259</strong> (1,000 x 1.10⁴⁰), a 45x return with no extra deposits. The catch is the long horizon and a high assumed rate, which are not guaranteed. This shows why starting early beats starting big. Model your own term in the <a href="/future-value-calculator/">future value calculator</a>.

How do I use future value to compare a lump-sum offer of $15,000 today versus $20,000 in 6 years?

Grow today's cash to the same future date, then compare. At a 5% return, $15,000 today becomes <strong>$20,101</strong> in 6 years (15,000 x 1.05⁶), which slightly beats the $20,000 offered later. So $15,000 now is marginally better at 5%. If you expect a lower return, the future $20,000 wins. The break-even return here is just under 5%. This is the core use of FV for offers.

What future value does $100,000 reach in 15 years at 5%?

A $100,000 lump sum at 5% for 15 years grows to about <strong>$207,893</strong>, slightly more than doubling. The calculation is 100,000 x 1.05¹⁵ = $207,892.82. With no added contributions, the entire $107,893 gain comes from compounding the original balance. This roughly matches the <a href="/rule-of-72-calculator/">Rule of 72</a> estimate that 5% doubles money in about 14.4 years.

How is future value different from present value?

Present value and future value are inverses of the same equation. FV grows money forward (FV = PV x (1 + r)ⁿ); present value discounts money backward (PV = FV / (1 + r)ⁿ). For example, $26,765 is the future value of $20,000 at 6% over 5 years, and conversely $20,000 is the present value of $26,765 under the same terms. Use the <a href="/present-value-calculator/">present value calculator</a> to discount instead of grow.

What is the future value of $50,000 at 4% for 10 years in a conservative account?

A $50,000 lump sum at 4% for 10 years grows to about <strong>$74,012</strong> (50,000 x 1.04¹⁰), a $24,012 gain with no contributions. Any specific bank's posted rate changes constantly, so plug in whatever rate your account actually pays. A lower 4% return reaches far less than 7% would over the same term, showing how sensitive FV is to the rate you assume.

Can future value be lower than the amount I started with?

Yes, future value drops below your principal whenever the growth rate is negative. If $50,000 loses 2% a year for 10 years, FV = 50,000 x 0.98¹⁰ = <strong>$40,854</strong>, a $9,146 loss in nominal terms. Even a positive nominal rate can produce a real loss if inflation runs higher than your return. The FV formula works for any rate; a negative r simply shrinks the balance.

How much will $20,000 grow to in 25 years at 9%?

A one-time $20,000 deposit at 9% for 25 years reaches about <strong>$172,462</strong> (20,000 x 1.09²⁵), more than 8x the original. No new money is added, so all $152,462 of gain is compounding. A 9% long-run rate is optimistic and not guaranteed, so treat it as a high-end scenario. Compare gentler rates side by side in the <a href="/investment-calculator/">investment calculator</a>.

What is the future value of $200,000 over 30 years at 6%?

A $200,000 lump sum at 6% for 30 years grows to about <strong>$1,148,698</strong>, crossing seven figures from a single deposit. The math is 200,000 x 1.06³⁰ = $1,148,698.23, with the entire $948,698 gain from compounding. Remember this is nominal; at 3% inflation its real purchasing power is closer to $473,000 in today's dollars. See the <a href="/millionaire-calculator/">millionaire calculator</a> for goal-based planning.

Guides & articles

• Future Value of a Lump Sum, Explained
• Using Future Value to Compare Lump-Sum Offers

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