You are signed up for Comcast internet service. This service requires a physical

Question

You are signed up for Comcast internet service. This service requires a physical device, a cable modem, to connect you to the provider's internet service. You have two options:

1. buy the cable modem on the internet, this will cost about $100

2. rent the cable modem from the provider, this will cost about $8/month.

Assume the relevant investment rate of return is 0.6% APR on your money (this is petty cash, and would just be sitting in your high-interest savings account at best). Assume the lifetime of the device is 4 years. What is net benefit to you of buying the device as compared to renting it?

Hint: find the present value of all the estimated rent payments for the lifetime of the device. compare to the present value of buying it outright. the 'benefit' may be positive or negative, depending on whether you give up more present-wealth renting or buying.

Explanation / Answer

Annual percentage rate = .6%

monthly percentage rate = .6/12*100 = .05%

present value of monthly payments = PVAF@.05% for 48 months * monthly rentals

47.416 * 98 = 379.33

present worth of rental payment 379.33

present value of purchase = 100

100 - 379.33 = 279.33

machine should be purchased

months present value @.05% 1 0.99950025 2 0.99900075 3 0.998501499 4 0.998002498 5 0.997503746 6 0.997005243 7 0.99650699 8 0.996008985 9 0.995511229 10 0.995013723 11 0.994516464 12 0.994019455 13 0.993522693 14 0.99302618 15 0.992529915 16 0.992033898 17 0.991538129 18 0.991042608 19 0.990547334 20 0.990052308 21 0.989557529 22 0.989062998 23 0.988568713 24 0.988074676 25 0.987580886 26 0.987087342 27 0.986594045 28 0.986100994 29 0.98560819 30 0.985115633 31 0.984623321 32 0.984131255 33 0.983639436 34 0.983147862 35 0.982656533 36 0.982165451 37 0.981674613 38 0.981184021 39 0.980693674 40 0.980203573 41 0.979713716 42 0.979224104 43 0.978734736 44 0.978245614 45 0.977756735 46 0.977268101 47 0.976779711 48 0.976291566 PVAF 47.41686892

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