Question

4) Jennifer will need to pay $200 at the end of every month for the next 12 months, except for the payment of the 10th month. What is the value assuming a rate of 4% compounded quarterly? a) 2261.01 b) 2155.49 c) 2199.02 d) 237.88

Answer 1

Correct Option B 2155.49

Step - 1

First of all we will calculate the effective annual rate

Effective Annual Rate = (1 + R/N)^N - 1

where

R = Annual Nominal Rate

N = Number of compounding period

Effective Annual Rate = (1 + R/N)^N - 1

Effective Annual Rate = (1 + 0.04/4)^4 - 1 = 4.0604%

Step 2 - Calculation of present value factor

To calculate the present value factor we have to use the following formulae

Present Value factor for 1 month = 1.040604 ^ (1/12) = 1.003322

Present Value factor for 2 month = 1.040604 ^ (2/12) = 1.006656

Month	Present Value Factor
1	1.003322
2	1.006656
3	1.010000
4	1.013356
5	1.016722
6	1.020100
7	1.023489
8	1.026889
9	1.030301
10	1.033724
11	1.037158
12	1.040604

Step 3 - Calculation of present value of all the cash flows

Month	Cash Flow	Present Value Factor	Present Value
1	200	1.003322	199.34
2	200	1.006656	198.68
3	200	1.010000	198.02
4	200	1.013356	197.36
5	200	1.016722	196.71
6	200	1.020100	196.06
7	200	1.023489	195.41
8	200	1.026889	194.76
9	200	1.030301	194.12
10		1.033724	0.00
11	200	1.037158	192.83
12	200	1.040604	192.20
		Present Value	2,155.49

Present Value of cash flow = 2155.49