Question

Jennifer will need to pay $200 at the end of every month for the next 12 months, except for the payment of the 5th month. What is the present value, assuming a rate of 4%, compounded quarterly?

a.2,348.97

b.2,160.06

c.2,254.09

d.2,152.26

Answer 1

Answer:
Calcualtion of present value of monthly payment.
Step 1: Calculation of effective interest rate
= (1+ nominal rate/4)^4 - 1
= (1 + 0.04/4)^4 -1
= (1.01)^4 -1
= 1.04060 -1
= 0.0406	or 4.06%
Monthly rate = 4.06%/12 = 0.3383%
Step 2: calculation of present value
Year	Cash inflows	Present value factor @0.3383%	Present value
1	$200	0.9966	199.33
2	$200	0.9933	198.65
3	$200	0.9899	197.98
4	$200	0.9866	197.32
5	$0	0.9833	0.00
6	$200	0.9799	195.99
7	$200	0.9766	195.33
8	$200	0.9733	194.67
9	$200	0.9701	194.01
10	$200	0.9668	193.36
11	$200	0.9635	192.71
12	$200	0.9603	192.06
		Total	2151.40
Present value as per the given options is (Answer is d)	$2,152.26