What Is the Time Value of Money (TVM)? Formula and Examples

By Markets & Investing DeskUpdated Nov 10, 2026

Definition

The time value of money is the principle that a dollar available today is worth more than the same dollar received later, because money held now can be invested to earn a return.

Key takeaways

TVM connects present value (what money is worth now) and future value (what it grows to) through an interest rate and a time period.
Compounding moves money forward in time. Discounting moves it backward.
The formula shows how value changes over time rather than producing a single "TVM" number.
TVM underpins valuation, capital budgeting, loan pricing and retirement planning.

The time value of money (TVM) is the principle that a sum of money available today is worth more than the same nominal sum received in the future, because money held now can be invested to earn a return. A dollar promised for tomorrow cannot be put to work until it arrives, and inflation may erode what it buys in the meantime.

How the time value of money works

Three forces explain why timing changes value.

Earning potential. Money deposited in an interest-bearing account earns interest, and that interest is added to the principal and earns interest of its own. This is compound interest, the mechanism behind TVM. The longer money compounds, the larger the gap between its present and future value.

Inflation. Prices for goods and services tend to rise, so a fixed dollar amount buys less later. Suppose $1,000 is left in a drawer for three years and, as a hypothetical, inflation runs at 3% a year. Its purchasing power falls to about $915 in today’s terms ($1,000 ÷ 1.03³). The owner also forgoes whatever the money could have earned.

Opportunity cost. Choosing to receive money later means giving up what it could have earned in the meantime. Even a payment that is certain to arrive carries this cost, which is why the future sum is worth less today.

Time value of money formula

The general future value formula is:

FV = PV × (1 + i/n)^(n × t)

where:

FV = future value of the money
PV = present value of the money
i = annual interest rate (as a decimal)
n = number of compounding periods per year
t = number of years

When interest compounds once a year (n = 1), the formula simplifies to FV = PV × (1 + i)^t.

Present value form

Rearranging the same equation shows what a future amount is worth today:

PV = FV ÷ (1 + i/n)^(n × t)

The rate used here is called the discount rate. A higher discount rate or a longer wait produces a lower present value.

Annuities and perpetuities

Many real cash flows are a series of payments rather than one lump sum, so the formula takes different forms. With a payment PMT each period and a periodic rate r:

Present value of an ordinary annuity (payments at the end of each period, for N periods): PV = PMT × [1 − (1 + r)^−N] ÷ r
Future value of an ordinary annuity: FV = PMT × [(1 + r)^N − 1] ÷ r
Present value of a perpetuity (payments that continue indefinitely): PV = PMT ÷ r

Hypothetical example: $1,000 received at the end of each year for five years, discounted at 6%, has a present value of about $4,212. Five payments total $5,000, but the later ones are worth progressively less today.

Examples of the time value of money

All examples below are hypothetical and assume a fixed rate with no fees or taxes.

Future value of a lump sum

Invest $10,000 for one year at 10% compounded annually:

FV = $10,000 × (1 + 0.10/1)^(1 × 1) = $11,000

Effect of compounding frequency

Keep the same $10,000, 10% rate and one-year period, but compound more often:

Compounding	Calculation	Future value
Annually	$10,000 × (1 + 0.10)^1	$11,000.00
Quarterly	$10,000 × (1 + 0.10/4)^4	$11,038.13
Monthly	$10,000 × (1 + 0.10/12)^12	$11,047.13
Daily	$10,000 × (1 + 0.10/365)^365	$11,051.56

More frequent compounding raises the ending value because interest begins earning interest sooner. The gains shrink as frequency rises: moving from monthly to daily adds about $4 here. This is why a quoted annual rate and the effective annual yield can differ, and why comparing two products requires knowing how often each compounds.

Present value of a future payment

How much must be invested today at 7% compounded annually to have $5,000 in one year?

PV = $5,000 ÷ (1 + 0.07)^1 = $4,672.90

Comparing two projects

A business can choose between Project A, which pays $1 million in year one, and Project B, which pays $1 million in year five. Otherwise they are identical. Using a hypothetical 8% discount rate:

Project A: $1,000,000 ÷ 1.08 = about $925,926
Project B: $1,000,000 ÷ 1.08⁵ = about $680,583

The nominal payouts match, but Project A is worth roughly $245,000 more in present-value terms because its cash arrives four years earlier.

How the time value of money is used in finance

TVM is the foundation of most valuation and planning work:

Valuation. Discounted cash flow (DCF) analysis estimates what a business or asset is worth by discounting its expected future cash flows to today.
Capital budgeting. Net present value (NPV) subtracts the upfront cost of a project from the present value of its future cash flows. The internal rate of return (IRR) is the discount rate at which NPV equals zero.
Choosing a discount rate. Companies often discount project cash flows at their weighted average cost of capital (WACC), which reflects what investors and lenders require.
Loans and bonds. Mortgage payments, loan amortization schedules and bond prices are annuity and present-value calculations.
Personal and retirement planning. Savers use future value to estimate how contributions grow. Pension fund managers use present value to judge whether assets will cover benefits owed decades from now.

TVM applies to costs as well as income. Planners discount future outlays too, so expenses spread over many years have a different present cost than the same total paid upfront.

Opportunity cost is what TVM measures. TVM puts a number on that cost through a rate and time period.

Inflation is one input into the rate. A nominal interest rate includes expected inflation, and the real rate is roughly the nominal rate minus inflation. TVM still applies when inflation is zero, because money can earn a real return.

Profitability measures such as net income or return on equity (ROE) report results for a period without weighting when cash arrives. Two projects with equal total profit can have very different present values. Simple payback period analysis also ignores TVM. NPV, IRR and DCF are the standard methods that account for it.

Limitations of the time value of money

It assumes a positive return. The basic model does not account for capital losses or negative interest rates, both of which can occur.
The discount rate is an estimate. Small changes in the rate can shift present values significantly, especially over long periods.
Constant rates are a simplification. Real returns and inflation vary from year to year.
Risk must be added separately. The formula treats a future cash flow as certain unless risk is built into the rate or the cash flow estimates.
Fees and taxes are excluded unless the calculation includes them explicitly.

FAQs

Is there a quick way to estimate compounding?

The Rule of 72 approximates how long money takes to double: divide 72 by the annual percentage rate. At 8%, money roughly doubles in nine years. The shortcut is less accurate at very high or very low rates.

The Bottom Line

Anyone comparing loans, savings products, investment projects or retirement plans relies on the time value of money, because the timing of cash changes what it is worth today. Converting future amounts to present value with a stated rate and compounding frequency allows a fair comparison of payments that arrive at different times. Results depend heavily on the chosen discount rate, and risk, fees and taxes must be built into the calculation separately.