Saving & investing
Time value of money: Definition, Formula and Example
The time value of money compares cash at different dates by accumulating or discounting it at a specified rate.
Scope: General financial concept; examples are hypothetical.
Other names and related labels: Present value and future value; TVM.
How it works
Present value translates future money into an equivalent amount at an earlier date. Future value compounds a current amount forward. The chosen rate reflects the comparison you are making; inflation, investment return and a risk-adjusted discount rate are not automatically interchangeable.
Future value = present value × (1 + rate)^periods; present value = future value / (1 + rate)^periods
Rates and periods must match. These are lump-sum formulas; separate deposits and withdrawals require separate timing.
$1,210 due in two years
Use a hypothetical 10% annual discount rate.
- Present value: $1,210 / 1.10² = $1,000.
- Reverse check: $1,000 × 1.10² = $1,210.
At the stated rate, $1,210 in two years has a present value of $1,000.
Two full annual periods; one payment; no fees or uncertainty in the stated cash flow.
Try these example inputsDiscounting does not make a risky payment certain
A higher chosen discount rate reduces present value. That arithmetic does not establish the correct rate or guarantee payment. Compare cash flows in the same currency and use nominal cash flows with a nominal rate, or real cash flows with a real rate.
Explore with a calculator
- Present Value Calculator
Discount a lump sum or regular payments.
- Future Value Calculator
Compound a lump sum and modeled deposits.
- Finance Calculator
Solve standard time-value-of-money variables.
- Cash Back or Low Interest Calculator
Compare financing offers over their stated payment terms.
- Rent vs. Buy Calculator
Compare dated housing cash flows under the tool’s assumptions.
Sources and checks
Definition and example arithmetic checked . Sources explain the concepts; numerical examples use the assumptions stated above.
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