Time Value of Money: Comparing Money Across Time

Present value, or PV, is the value today of a future cash flow after applying an assumed rate and time period. Future value, or FV, is the value at a later date of money held or invested today after applying an assumed rate of return. These are two directions of the same comparison: moving money forward uses compounding, while moving it backward uses discounting.

With periodic compounding at a constant rate, future value is calculated as FV = PV × (1 + r)^n. Here, r is the rate per period and n is the number of periods. To calculate the present value of one future cash flow under the same assumptions, use PV = FV ÷ (1 + r)^n. The rate and the number of periods must use matching units: for example, a rate per period should be paired with the corresponding number of periods.

First, identify the cash flow, its amount, and the date when it occurs. Second, draw a timeline showing the relevant dates and periods. Third, decide whether you are moving the amount forward to find future value or backward to find present value. Fourth, identify the rate per period and the number of periods. Finally, apply the matching formula and state the assumptions. For example, if PV is 1,000, r is 5% per period, and n is 2 periods, FV = 1,000 × (1.05)^2 = 1,102.50. Reversing the direction, a future cash flow of 1,000 has PV = 1,000 ÷ (1.05)^2, approximately 907.03.