Finance calculator

Free time value of money calculator

See what money is worth across time. Enter an amount, a rate, and a number of periods, then solve for future value (what today's money grows to) or present value (what future money is worth today) — with an optional payment each period, updated live, as you type.

InputsLive
Solve for
Present value (amount today)
$
Rate per period
%
Number of periods
Payment per period (optional)
$
Result
Future value
$1,628.89
What today's money grows to after compounding forward.
Starting amount$1,000.00
Rate per period5%
Periods10

Estimates only, based on the values you enter. Not financial advice.

Results are estimates. Consult a professional.

Definition

What is the time value of money?

The time value of money (TVM) is the principle that a sum of money is worth more today than the same sum received in the future. Money you hold now can be invested to earn a return, so a dollar today can become more than a dollar tomorrow — and, in reverse, a dollar promised years from now is worth less than a dollar in your hand. This time value of money calculator puts that principle to work: enter an amount, a rate, and a number of periods and it returns either what today's money grows to (future value) or what future money is worth today (present value), the moment you type.

Three forces drive the gap between present and future dollars. Earning power — money invested compounds and grows. Inflation — prices rise, so a future dollar buys less than today's. Risk and opportunity cost — a promise to pay later carries uncertainty and ties up money you could have used elsewhere. TVM is the single idea that prices all three into one comparable number.

What a future sum of money is worth today, once it has been discounted back at a given rate.
What money invested today will be worth at a later date, once it has earned compound interest.
The interest rate or expected return per period — the engine that converts present dollars into future ones and back again.
The number of compounding or payment periods between today and the future date.
Formula

Time value of money formula

The time value of money rests on one core relationship, which links a present amount, a future amount, a rate, and a number of periods. For a lump sum with an optional level payment each period, the future value is:

FV = PV × (1 + r)^n + PMT × [ ((1 + r)^n 1) / r ]
PV = FV ÷ (1 + r)^n + PMT × [ (1 (1 + r)^n) / r ]
r = periodic rate, n = number of periods, PMT = payment per period

The two equations are mirror images. Future value compounds forward — it multiplies by (1 + r)^n. Present value discounts back — it divides by the same factor. Everything else in finance, from a savings projection to a bond price, is built on these two operations applied to one or more cash flows.

When the rate is 0%, the growth factor (1 + r)^n equals 1 and the payment term collapses to PMT × n — money simply stacks up without compounding. The calculator handles that edge case so the result never breaks.
Inputs

The five variables of the time value of money

Every time value of money problem is built from the same five variables. Give the calculator any four and it solves for the fifth — this tool focuses on the two most-searched of those: solving for future value and solving for present value.

  1. Present value (PV) — the amount today, at time zero. Your starting deposit or the lump sum you hold now.
  2. Future value (FV) — the amount at the end, after compounding and any payments. Your target balance or projected total.
  3. Rate (I/Y) — the interest rate or rate of return per period. It must match the period length you use.
  4. Number of periods (N) — how many compounding or payment periods sit between today and the future date.
  5. Payment (PMT) — an optional level amount added (or paid) each period, on top of the lump sum.

The cardinal rule is to keep the rate and the period count on the same frequency. For monthly contributions, divide the annual rate by 12 and multiply the years by 12; for annual ones, use the annual rate and the number of years directly. Mixing an annual rate with a monthly period count is the single most common time-value error.

Worked example

A worked example using the time value of money calculator

Example: $1,000 invested for 10 years at 5%

Priya has $1,000 today and wants to know what it will be worth in 10 years at a 5% annual return. Here is how the calculator walks through the future-value calculation, one period at a time.

Step 1 — Enter the inputs

Priya leaves the mode on future value, sets the present value to $1,000, the rate to 5%, and the number of periods to 10. She leaves the optional payment at $0 — this is a single lump sum.

Step 2 — Apply the formula

FV = 1,000 × (1 + 0.05)^10
FV = 1,000 × 1.628895
FV = 1,628.89

Step 3 — Read the result

$1,628.89 future value
Priya's $1,000 grows by $628.89 over the decade — all of it compound interest, since she added nothing along the way. The calculator shows the future value, the starting principal, and the rate and term side by side.

Now run it backwards. Switch the mode to present value, enter $1,628.89 as the future amount, keep 5% and 10 periods, and the calculator returns $1,000 — the lump sum you would accept today instead of that future payout. Present value and future value are the same calculation pointed in opposite directions. All figures here are computed by this calculator using the formula above.

Two directions

Present value vs. future value

Present value and future value are the two sides of the time value of money. Future value answers “what will money I have today grow to?” Present value answers “what is money I will receive later worth right now?” Future value compounds a present amount forward; present value discounts a future amount back. For any positive rate, the future value is always larger than the present value — compounding adds growth, discounting strips it away.

Future valuePresent value
Question it answersWhat will today's money become?What is future money worth today?
DirectionCompounds forwardDiscounts back
OperationMultiply by (1 + r)^nDivide by (1 + r)^n
Typical useProjecting savings or investment growthPricing a future payout or income stream

The same rate and term; only the direction of the calculation — and therefore the number — differs.

To work a single direction in more depth, pair this with the present value calculator and the future value calculator. For a stream of equal payments rather than a lump sum, use the present value of an annuity and future value of an annuity tools.

Mechanics

Discounting vs. compounding

Compounding and discounting are the two engines of the time value of money, running in opposite directions. Compounding earns a return on both your principal and the interest already earned, growing a present sum into a larger future one. Discounting is the reverse: it strips that growth back out to find what a future sum is worth today.

  • Compounding — $1,000 invested at 5% for 10 years grows to $1,628.89. Interest earns interest, so the balance accelerates the longer it is left.
  • Discounting — $1,628.89 expected in 10 years, discounted at 5%, is worth $1,000 today. The further off the payment and the higher the rate, the more it shrinks.

The rate used to discount is often called the discount rate or the opportunity cost of capital: it represents the return you could earn on money instead of waiting. A higher discount rate makes future cash flows worth less today, which is why rising interest rates lower the present value of bonds, pensions, and any long-dated promise to pay.

Why it matters

Why the time value of money matters

The time value of money is the single most important idea in finance because almost every money decision is a trade between dollars at different points in time. Whenever you compare an amount now against an amount later, TVM is the tool that puts them on equal footing.

  • Inflation — prices drift upward, so a dollar in the future buys less than a dollar today. TVM quantifies exactly how much earning power you lose by waiting.
  • Opportunity cost — money received now can be invested immediately; money received later forfeits every period of growth in between.
  • Risk — a future payment may never arrive. Discounting builds that uncertainty into a lower present value.
  • Liquidity and flexibility — cash in hand can be spent, saved, or redirected at once; a future claim cannot.

This is why a lottery jackpot paid over 30 years is worth far less than its headline number, why a lender charges interest, and why "would you rather have $100 today or $110 next year?" has no single right answer — it depends entirely on the rate. Pair this with the opportunity cost calculator to see the growth a delayed dollar gives up.

Applications

What the time value of money is used for

Because it converts any cash flow to a common point in time, TVM underpins nearly every quantitative decision in personal finance, investing, and business. Common uses include:

  • Retirement and savings planning — projecting what a balance or regular contribution becomes by a target date.
  • Investment valuation — discounting a company's future cash flows to estimate what it is worth today (the basis of discounted cash flow analysis).
  • Loan and mortgage pricing — every payment schedule is a present value set equal to the amount borrowed.
  • Lump sum vs. instalments — deciding whether to take a pension, settlement, or prize as a lump sum or a stream of payments.
  • Capital budgeting — comparing projects whose costs and returns land in different years on a like-for-like basis.

In every one of these, the question is the same: are dollars arriving at different times truly comparable? The time value of money says no — and gives you the rate-and-time adjustment that makes them comparable.

Limitations

Assumptions and limitations

A time value of money figure is only as good as the assumptions behind it. A few are worth keeping in mind:

  • A constant rate. One fixed rate is applied to every period. Real returns and interest rates vary, so treat the output as a planning estimate, not a guarantee.
  • Compounding matches the period. The rate and the period count must use the same frequency; this calculator compounds once per period you enter.
  • Level, end-of-period payments. The payment term assumes an equal amount paid at the end of each period (an ordinary annuity). Growing or front-loaded payments need a different model.
  • No taxes, fees, or inflation adjustment. The figure is gross. To see what a future dollar buys in today's terms, discount at an inflation rate instead of (or alongside) a return.
Methodology

Formula sources and methodology

The core relationship FV = PV × (1 + r)^n + PMT × [((1 + r)^n − 1) / r], and its rearrangement to solve for present value, are standard time-value-of-money results taught in every corporate finance curriculum. The calculator applies the lump-sum factor and the ordinary-annuity factor directly, falling back to PMT × n when the rate is 0%, so its output matches the standard reference implementations and the Excel FV and PV functions.

Corporate Finance Institute — Time Value of Money (FV = PV × (1 + i)^n).CalculatorSoup — Time Value of Money Calculators (present value, future value, compounding and discounting).
Questions

Frequently asked questions about the free time value of money calculator

A time value of money calculator is a free online tool that helps you calculate the time value of money — what today's money grows to (future value) or what future money is worth today (present value) — from an amount, a rate, and a number of periods, with an optional payment. The time value of money is the principle that a dollar today is worth more than a dollar later, because it can be invested. Future value compounds a present amount forward; present value discounts a future amount back. It runs entirely in your browser with instant results and no sign-up.
The time value of money is the principle that a sum of money is worth more today than the same sum in the future, because money you have now can be invested to earn a return. A dollar today can grow into more than a dollar tomorrow, and a dollar promised in the future is worth less than a dollar in hand once you account for earning power, inflation, and risk.
The core formula is FV = PV × (1 + r)^n + PMT × [((1 + r)^n − 1) / r], where PV is the present value, FV the future value, r the rate per period, n the number of periods, and PMT an optional level payment. To find present value instead, rearrange it: PV = FV ÷ (1 + r)^n + PMT × [(1 − (1 + r)^−n) / r]. Drop the PMT term for a single lump sum.
Three reasons. Money today can be invested immediately to earn interest, so it compounds and grows. Inflation erodes purchasing power, so a future dollar buys less than today's. And a future payment carries risk and forfeits flexibility — it might not arrive, and you cannot use it in the meantime. The time value of money prices all three into one comparable number.
Future value is what money you have today grows to after compounding forward, found by multiplying by (1 + r)^n. Present value is what money you will receive later is worth today, found by discounting back — dividing by the same (1 + r)^n. For any positive rate, the future value is always larger than the present value.
Present value (PV), future value (FV), the rate per period (I/Y), the number of periods (N), and the payment per period (PMT). Given any four, you can solve for the fifth. This calculator focuses on the two most-searched cases: solving for future value and solving for present value.
Compounding grows a present amount into a larger future one by earning a return on both principal and accumulated interest — it moves money forward in time. Discounting is the reverse: it strips that growth back out to find what a future amount is worth today. Compounding finds future value; discounting finds present value.
About

About this time value of money calculator

This time value of money calculator runs entirely in your browser. Every figure you enter stays on your device — nothing is sent to a server, logged, or shared. It compounds a present amount forward with FV = PV × (1 + r)^n plus the ordinary-annuity payment term, discounts a future amount back with the mirror-image formula, and falls back to a straight PMT × n when the rate is 0% — all updating instantly as you type.

Calculators Cloud offers 400+ free tools with no sign-up. The whole Finance calculators shelf includes Present value, Future value, and Compound interest tools alongside this one. Or browse the full calculator directory.

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