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 $10/month.

Assume the relevant investment rate of return is 0.7% 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 6 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.

Answer 1

Given, lifetime of device= 6 years. Investment rate of return= 0.7% APR

Option 1: Buy at a cost of $100

Option 2: Rent at $10/month

It is assumed that rent is paid at the beginning each month. Monthly rent is equivalent to annuity due. Present value of rent stream for 10 years= $ 705.30 Calculated as follows:

Net benefit of buying the device= $705.30-$100 = $605.30