Final answer:
The correct answer is option c, indicating that the shorter the time period, the higher the present value of a stated future value.
Step-by-step explanation:
The correct answer is option c: The shorter the time period, the higher the present value of a stated future value. To understand the relationship between time period and present value, consider that present value is determined by discounting the future value back to the present. This discounting process is affected by the length of the time period and the interest rate.
If we have a longer time period before a future sum is received, the present value of that sum will be smaller because the money has more time to be discounted by the interest rate over a longer period. Conversely, if the time period is shorter, there is less time for the discounting effect to occur, resulting in a higher present value. This concept is based on the present value discounting principle which states that a dollar today is worth more than a dollar tomorrow because of the potential earning capacity.
The other options can be assessed by the same logic. Option a is correct because with compound interest, the amount of interest earned increases over time, resulting in a greater future value. Option b is incorrect because it's the inverse of option a; a shorter time period leads to a higher present value due to less time for discounting. Lastly, option d is incorrect as the present value decreases the longer the time period given the stated future value because of the impact of the interest rate over time.