What is the formula for present value PV given FV, rate i, and periods n?

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

Answer: (B)

The main idea here is discounting a future amount back to its present value using the per-period interest rate. If you know the future value after n periods, the present value is found by removing the growth factor (1+i) raised to n, so PV = FV / (1+i)^n. This comes from the basic relationship FV = PV*(1+i)^n, which shows how value grows with compounding. Solving for PV gives PV = FV/(1+i)^n.

For example, if you expect FV = 200 in 3 years at a 5% per-year rate, the present value is 200 / (1.05)^3 ≈ 173.50.

The other forms don’t fit because they either apply the rate incorrectly or count periods the wrong way: dividing by (1+i n) uses a linear, incorrect combination of i and n; multiplying by (1+i)^n would give you a future value from a present value, not the present value itself; and dividing by (1+i)^(n-1) discounts for one fewer period than intended.