Which formula correctly computes the present value of a future cash flow?

• A. PV = FV / (1 + r)^n
• B. PV = FV * (1 + r)^n
• C. PV = FV - r * n
• D. PV = FV / (1 - r)^n

Answer: (A)

The present value is found by discounting a future amount back to today, reflecting that money available now can earn interest over time. If a future cash flow is FV and the rate per period is r over n periods, the amount today (PV) is FV divided by the compounding factor (1 + r) raised to n: PV = FV / (1 + r)^n. This comes from the idea that FV = PV × (1 + r)^n, and solving for PV gives the division form. Remember to use r as a decimal (for example, 5% as 0.05).

For example, if you expect $110 in one year with a 10% rate, the present value is 110 / 1.10 = 100. The other forms aren’t correct for calculating present value: multiplying by (1 + r)^n would give the future value from a present amount, not the present value; subtracting r × n reduces FV linearly, which doesn’t account for compounding; and using (1 − r)^n in the denominator uses an incorrect discount factor.