The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant. A. TrueB. False

B. False

Explanation:

The present value of a future sum is the value in today's term of a sum of amount calculated by taking the future cash flow or amount and discounting it back to today's value using an appropriate discount rate and time period. The formula for present value of a sum of amount is,

PV = FV / (1+r)^t

Where,

The statement that " The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant. " is false as the present value falls in both the scenarios as can be seen by the following example.

Let FV be $5000.

r = 5%

t = 10

PV = 5000 / (1.05)^10

PV = $3069.57

Now if the r or discount rate is increased to 10% and other things remain constant,

PV = 5000 / (1.10)^10

PV = $1927.72

As a result of increasing discount rate, the PV falls.

Now taking the initial r or discount rate but increasing the time periods to 15 and other things remain constant,

PV = 5000 / (1.05)^15

PV = $2405.09

As a result, the PV also fell as compared to the initial PV.

answerreactive approach;