--- title: Time Value of Money Calculator (2026) — PV, FV & the cost of waiting | Allocate AI description: Free time value of money calculator. See how inflation erodes purchasing power, how invested dollars compound, and what waiting ten years to start really costs. canonical: https://allocateai.io/calculators/time-value site: Allocate AI — https://allocateai.io --- # Time Value of Money Calculator See how inflation erodes your purchasing power, why invested dollars grow exponentially, and the real cost of waiting to start. *This is the write-up of an interactive calculator. Use it at https://allocateai.io/calculators/time-value — the inputs, charts and year-by-year tables are on that page. The formulas are below.* > Returns are hypothetical and assume a constant annual rate compounded monthly. Real investment returns vary year to year and are not guaranteed. The S&P 500's historical average of about 10% is before inflation; real returns average about 7%. Inflation rates change. This calculator is for education, not financial advice. ## How it's calculated Compares investing now against waiting, holding everything else constant, so you can see the dollar cost of delay. - **Future value**: FV = PV × (1 + r)^t - **Present value**: PV = FV ÷ (1 + r)^t - **Monthly contributions**: FV = m × ((1 + r/12)^12t − 1) ÷ (r/12) - **Purchasing power**: $1 ÷ (1 + inflation)^t - **Cost of waiting**: FV(start now) − FV(start 10 years later) - Contributions are level and land at the end of each month - The annual return is fixed; compounding is monthly - No taxes or fees are taken out along the way - Both scenarios end on the same date — retirement age ## What is the time value of money? The time value of money is the idea that a dollar today is worth more than a dollar in the future. Two forces drive that gap. First, a dollar in hand today can be invested and earn a return, so by next year it has grown into something larger. Second, inflation steadily erodes purchasing power, so a dollar received a year from now buys slightly less than the same dollar would buy today. This concept sits underneath nearly every financial decision: whether to take a lump sum or payments over time, how to compare loans, what a future bonus is "really" worth, and how to value [investing](https://allocateai.io/calculators/compound-interest) today versus waiting a few years. It's also why retirement, mortgages, and bond pricing all use the same underlying math. In plain terms: money has a price tag attached to time. Comparing dollars from different points in time without adjusting for that price tag is like comparing prices in two different currencies without converting them. ## Present value vs. future value Present value (PV) is what a future amount of money is worth today. Future value (FV) is what a current amount is worth at some point in the future. The two are mirror images of the same equation. Future value: FV = PV × (1 + r)^n Present value: PV = FV ÷ (1 + r)^n Where **PV** is present value, **FV** is future value, **r** is the periodic rate (often annual), and **n** is the number of periods. Compounding moves a dollar forward in time (today → future); discounting moves a future dollar backward in time (future → today). They are the same idea applied in opposite directions. A worked example: $10,000 invested at 7% for 10 years grows to $10,000 × 1.07^10 = **$19,671.51**. Run backwards, $19,671.51 due in 10 years is worth exactly $10,000 today at a 7% discount rate. ## Why inflation matters Inflation reduces what a future dollar actually buys. A "real" return strips inflation out of the nominal return so you can see growth in purchasing power, not just dollar count. As a rough illustration: if an investment earns 7% in a year and inflation is 3%, the real return is roughly 4%. The portfolio grew by 7% on paper, but its purchasing power grew by about 4%. Over long horizons the effect compounds heavily. At 3% annual inflation, $100 today has roughly the purchasing power of about $74 in 10 years and about $55 in 20 years. That's why long-term plans like retirement need to be modeled in real (inflation-adjusted) terms — comparing a future nominal balance to today's lifestyle without adjusting overstates how far the money will go. ## How the time value of money shows up in real decisions Common examples: choosing a lump sum versus payments over time, weighing a lottery or pension election, deciding whether to pay down a loan early or invest the same dollars, and valuing a bonus or [RSU vest](https://allocateai.io/calculators/rsu-tax) that pays in a future year. In each case, comparing the options requires expressing them at the same point in time — either all as present value or all as future value. The calculator above lets you do exactly that: enter amounts, a rate, and a horizon, and compare what those dollars are worth at different points in time on equal footing. The same machinery is what powers retirement projections, mortgage amortization, and bond pricing under the hood. ## Frequently asked questions ### What is the time value of money in simple terms? It's the idea that a dollar today is worth more than the same dollar later because today's dollar can be invested and because inflation slowly chips away at future purchasing power. It's the basis for almost every financial calculation involving multiple points in time. ### What is present value? Present value is what a future cash flow is worth today, given an assumed rate of return. It answers: how much would I need today, invested at rate *r*, to grow into that future amount? The formula is PV = FV ÷ (1 + r)^n. ### What is future value? Future value is what a current amount of money will be worth at a specified point in the future, given a rate of return. It answers: if I invest this today at rate *r*, what will it grow to in *n* periods? The formula is FV = PV × (1 + r)^n. ### What discount rate should I use? It depends on the context. Often it's a relevant expected return (for example, a diversified market return) or a cost of capital (the rate at which you could borrow, or that an alternative investment would yield). There is no single right number — a higher rate makes future cash less valuable today, a lower rate makes it more valuable. This calculator is for education, not personalized advice. ### How does inflation affect the time value of money? Inflation reduces what each future dollar will buy. A “real” return subtracts inflation from the nominal return so you see growth in purchasing power instead of just dollar count. Over decades, even modest inflation meaningfully shrinks the real value of future dollars. ### Why is a dollar today worth more than a dollar tomorrow? Because you can put today's dollar to work — invest it, pay down debt, or earn interest — and because tomorrow's dollar will buy slightly less after inflation. Those two effects together make near-term money more valuable than identical money received later. ### Does this calculator account for taxes? No. Returns are shown before taxes and fees, which keeps the comparison between starting now and starting later clean. In a taxable account the gap would be somewhat smaller in dollars but the same in direction; in a 401(k) or IRA it applies as shown. This calculator and its explanations are educational and give estimates only — not investment, tax or legal advice. Real returns, inflation and tax outcomes vary; talk to a qualified professional about your own situation. ## More calculators - [Compound Interest Calculator](https://allocateai.io/calculators/compound-interest) — Project growth with contribution changes and lump sums - [FatFIRE Withdrawal Calculator](https://allocateai.io/calculators/fire-withdrawal) — Will the portfolio last? Tax-aware drawdown - [Mega Backdoor vs. Traditional 401k](https://allocateai.io/calculators/mega-backdoor-growth) — After-tax value of each over time - [After-Tax Income Calculator](https://allocateai.io/calculators/after-tax-income) — Real take-home after federal, state and FICA **See your own money compounding** Allocate reads your accounts, tracks your savings rate and net worth, and shows the plan in plain words — before you decide anything. [Get started](https://app.allocateai.io/signup) --- Allocate AI is a budgeting and financial-planning app: link your accounts, say what you want in plain words, and it writes the plan and stages every change for your approval. Read more at https://allocateai.io or see all pages in https://allocateai.io/llms.txt.