Question

Your grandfather has promised to give you​ $500 a year at the end of each of the next four years if you earn Cs or better in all of your courses each year. Using a discount rate of​ 7%, which of the following is correct for determining the present value of the​ gift?

a. PV = $500x7%x4
b. PV = $500x(PV factor, i=4%, n =7)
c. PV = $500x(Annuity PV factor, i=7%, n=4)
d. PV = $500x(Annuity PV factor, i=7%, n=4)

Answer 1

The correct answer is option (d) PV = $500x(Annuity PV factor, i=7%, n=4)

Step-by-step explanation:

Given data;

P = $500

rate (r) = 7%

years (n)= 4

The present value of goods is determined using the formula;

PV of annuity = P x Annuity present value factor----------------1

But,

Annuity present value factor = [1-(1+i)⁻ⁿ)]/i ------------2

Putting equation 2 into equation 2, we have

PV of annuity = P x Annuity present value factor

PV of annuity = P * [1-(1+i)⁻ⁿ)]/i -----------------------3

where;

PV = present value

i = rate

n = number of years

P = price

To calculate PV using equation 3, option (d) is the appropriate option

Answer 2

d. PV = $500x(Annuity PV factor, i=7%, n=4)

Step-by-step explanation:

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity.

Formula for Present value of annuity is as follow

PV of annuity = P x Present value factor

PV of annuity = P x [ ( 1- ( 1+ i )^-n ) / i ]

As discount rate is 7%, so

i = 7%

Number of payments is 4

n = 4