Question

You are scheduled to receive annual payments of $3,600 for each of the next 12 years. The discount rate is 8 percent. What is thedifference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?A.$2,170.39B.$2,511.07C.$2,021.18D.$2,027.94E.$2,304.96

Answer 1

Answer:

A. $2,170.39

Explanation:

First, we understand that what we are dealing with is Ordinary annuity which represents payments received at the end of each year

As such, The Present value of Ordinary annuity is calculated using the following formula

= Annuity amount x (1-(1+r)∧-n ) /r

Plugging this formula into the schedule given in the question ew have teh following

First, the present value of the payments received at the end of each year

= $3,600 x (1- (1.08∧-12) / 0.10

= $27,129.88

Secondly, the present valueof the payments received at the beginning of each year

= = $3,600 x (1- (1.08∧-11) / 0.10

= $25,700.27 + $3,600 (the amont recieved today)

Total PV = $29,300.27

Finally, find the difference between the PV of cash flow received at the beginning and PV of Cash flow received at the end=

= $29,300.27-  $27,129.88

= $2,170.39