The present value of a future payment is always greater than the payment. true false
The correct answer and explanation is:
Correct Answer: False
Explanation:
The present value (PV) of a future payment refers to how much that future sum of money is worth today, given a specific interest or discount rate. In most realistic economic scenarios, money today is worth more than the same amount in the future, due to inflation, opportunity cost, and risk factors. Therefore, the present value of a future payment is usually less than the actual payment amount to be received in the future.
Why Is This False?
Suppose someone offers you $1,000 to be paid 2 years from now. You would ask, “How much is that $1,000 worth today?” To find out, you’d calculate the present value using a formula such as: PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}
Where:
- FV = future value (e.g., $1,000)
- r = annual interest or discount rate (e.g., 5% or 0.05)
- n = number of years into the future (e.g., 2)
So if: PV=1000(1+0.05)2=10001.1025≈907.03PV = \frac{1000}{(1 + 0.05)^2} = \frac{1000}{1.1025} \approx 907.03
This means that $1,000 in two years is only worth about $907 today at a 5% discount rate. The longer the time or the higher the interest rate, the lower the present value.
Exceptions?
The only time when present value could equal the future payment is if the discount rate is zero (0%), meaning there is no time value of money. In that rare theoretical case, the present value equals the future value—but still not greater.
Conclusion:
Since the present value is calculated by discounting future cash flows, it is not greater than the future payment. Therefore, the statement is false.