Which formula represents Present Value of a future amount?

Which formula represents Present Value of a future amount?

• A. Future Values / (1+r)^n
• B. (1+r)^n / Future Values
• C. Future Values * (1+r)^n
• D. Future Values / r^n

Answer: (A)

Discounting a future amount back to today uses the time value of money. The present value is found by bringing the future sum back n periods at the period rate r, which gives PV = FV / (1 + r)^n. The factor 1/(1 + r)^n is the discount factor, converting future value into its today’s worth. For example, if you expect 110 in one period and the rate is 10%, the present value is 110 / 1.1 = 100. The other expressions either multiply by (1 + r)^n or divide by r^n, which would not reflect the correct today value.

Discounting a future amount back to today uses the time value of money. The present value is found by bringing the future sum back n periods at the period rate r, which gives PV = FV / (1 + r)^n. The factor 1/(1 + r)^n is the discount factor, converting future value into its today’s worth. For example, if you expect 110 in one period and the rate is 10%, the present value is 110 / 1.1 = 100. The other expressions either multiply by (1 + r)^n or divide by r^n, which would not reflect the correct today value.