The time value of money means a dollar available today can have a different value from a dollar received later because of earning potential, inflation, risk and liquidity. It provides the mathematical foundation for loans, investments, leases, retirement saving and capital budgeting.
Future value of one amount
FV = PV × (1 + r)n, where PV is the amount today, r is the rate per period and n is the number of periods.
If $10,000 earns 5% annually for three years, FV = $10,000 × 1.053 = $11,576.25. This assumes annual compounding and no taxes or fees.
Present value of one amount
PV = FV ÷ (1 + r)n. If $11,576.25 is received in three years and the appropriate annual discount rate is 5%, its present value is $10,000.
Match rate and period
| Payment timing | Rate treatment | Number of periods |
|---|---|---|
| Annual | Annual rate | Years |
| Monthly | Compatible monthly rate | Months |
| Quarterly | Compatible quarterly rate | Quarters |
Do not divide an effective annual rate by 12 and call it an effective monthly rate without checking the convention. Nominal rate, effective rate and APR are not interchangeable.
Value a level annuity
For equal end-of-period payments, the present value of an ordinary annuity is Payment × [1 − (1 + r)−n] ÷ r. Payments at the beginning of each period form an annuity due and are worth more, all else equal.
Use discount rates carefully
The discount rate should reflect the decision and cash-flow risk. A contractually certain government payment and a speculative startup forecast should not automatically use the same rate. Keep cash flows and discount rates consistent for inflation, tax and currency. Test sensitivity rather than hiding value behind one rate.
Apply TVM to decisions
- Compare loan payment streams and balloon amounts.
- Calculate the present value of leases or contracts.
- Evaluate equipment using net present value.
- Estimate savings required for a future goal.
- Convert enterprise cash-flow forecasts into present value.
For capital investments, connect the math to strategic financial decisions. A positive NPV still depends on reliable incremental cash-flow assumptions.
Common mistakes
Watch for beginning-versus-end timing, inconsistent periods, omitted fees, mixing real and nominal amounts, treating forecasts as guaranteed, forgetting terminal cash flow and rounding too early. Use a timeline and independently recalculate a sample.
Frequently asked questions
Why is money today usually worth more?
It can be used or invested sooner and avoids some delay and uncertainty, though the appropriate value depends on risk and alternatives.
What happens when the discount rate rises?
The present value of future positive cash flows falls, all else equal.
Is compound interest always beneficial?
It benefits a saver earning returns but increases a borrower’s obligation when interest compounds.
Sources reviewed
Last reviewed: August 15, 2026. Examples are educational and exclude product-specific fees, taxes and risks.