Time Value of Money: Why a Dollar Today Is Worth More Than Tomorrow

The Core Concept

A dollar today is worth more than a dollar in the future because money available now can be invested to earn returns. This principle — the time value of money — underlies virtually all of finance: investment valuation, loan pricing, retirement planning, and capital budgeting.

Future Value

FV = PV × (1 + r)^n

Where PV = present value, r = interest rate per period, n = number of periods.

Example: $10,000 invested at 7% annually for 20 years: FV = $10,000 × (1.07)^20 = $38,697

Present Value

The inverse: what is a future sum worth today?

PV = FV ÷ (1 + r)^n

Example: What is $50,000 to be received in 10 years worth today at a 6% discount rate? PV = $50,000 ÷ (1.06)^10 = $50,000 ÷ 1.791 = $27,919

Net Present Value (NPV)

NPV = Sum of PV of all future cash flows − Initial investment. Used to evaluate whether an investment creates value. Positive NPV = investment earns more than the discount rate. The discount rate typically reflects either cost of capital or opportunity cost (what else you could earn).

Practical Applications

Should I take the $500,000 lottery lump sum or $25,000/year for 30 years? NPV calculation: the annuity is worth far less than face value.
Is paying $2,000 extra for a more efficient appliance worth it at $200/year in savings? Break-even + NPV analysis tells you.
Should I pay off my mortgage early? Compare the mortgage rate (certain return) to expected investment returns (uncertain but historically higher).

Frequently Asked Questions

What discount rate should I use for personal financial decisions?

Common approaches: use your mortgage rate (certain return from payoff), use expected stock market return (~7% real after inflation), or use your weighted cost of capital (average of all your debt and investment returns). For retirement calculations, 6–7% real return is a conservative but reasonable assumption.

How does inflation relate to time value of money?

Inflation erodes purchasing power over time — $1,000 today buys more than $1,000 in 10 years at any positive inflation rate. Real interest rate = Nominal rate − Inflation rate. When comparing dollars across time, always clarify whether you're using nominal or real (inflation-adjusted) values.