Final answer:
When the number of compounding periods increases, the time value of a cash flow at the same nominal annual rate increases. This is due to interest being compounded more frequently, which allows for interest to be earned on previously accumulated interest. The correct option is A.
Step-by-step explanation:
The student's question is asking about the impact on the time value of money when the number of interest compounding periods increases. If the nominal annual rate remains the same and the number of compounding periods increases, the time value of the cash flow would increase.
This happens because compounding interest more frequently allows for interest to be calculated on the previously earned interest, leading to a higher overall amount. For example, if you have $100 in an account with an annual interest rate of 10%, compounded annually, you will have $110 after one year.
However, if the interest is compounded semi-annually (twice a year), you would have a little more than $110 at the end of the year, because you're earning interest on the initial amount plus the interest from the first half of the year in the second half of the year.
Therefore, the correct answer from the provided options would be A. Time value increases.