The Time Value of Money: Present and Future Value

Money has time value for three fundamental reasons: opportunity cost, inflation, and uncertainty. If you hold $100,000 today, you can invest it — in a savings account, a Treasury bond, or a rental property — and earn a return. That potential return is the opportunity cost of waiting. Inflation erodes purchasing power over time; the Bureau of Labor Statistics reports that the U.S. Consumer Price Index averaged 3.2% annually from 1926 through 2023, meaning a dollar in 1926 would need over $17 to match its purchasing power today.

Uncertainty is the third driver: the further into the future a cash flow occurs, the less certain you can be that it will materialize. A signed lease payment due next month is far more reliable than a projected rent increase five years from now. Together, these three forces mean rational investors demand compensation — a discount rate — for deferring consumption.

Future value (FV) answers the question: "If I invest a sum today at a given rate, how much will it grow to?" The formula is FV = PV × (1 + r)^n, where PV is the present value, r is the periodic interest rate, and n is the number of compounding periods. For example, $100,000 invested at 7% annually for 10 years grows to $100,000 × (1.07)^10 = $196,715.

Compounding frequency matters. The same $100,000 at 7% compounded monthly for 10 years yields $100,000 × (1 + 0.07/12)^120 = $200,966 — roughly $4,251 more than annual compounding. This difference, driven by earning interest on interest more frequently, becomes significant over longer time horizons and is why banks quote both nominal rates and annual percentage yields (APY).

Present value (PV) is the mirror image of future value. It answers: "What is a future cash flow worth today?" The formula is PV = FV / (1 + r)^n. If you expect to receive $200,000 in 10 years and your required return is 7%, the present value is $200,000 / (1.07)^10 = $101,670. This means you should pay no more than $101,670 today for that future payment.

Present value is the workhorse of real estate valuation. When investors estimate a property's worth using the income approach, they discount projected net operating income (NOI) and a terminal sale price back to today using a discount rate that reflects the investment's risk. A higher discount rate produces a lower present value, reflecting greater risk or a higher required return.