Question 4 7 marks You currently pay 80 per month for cable

Question 4: (7 marks) You currently pay $80 per month for cable TV (Basic Service, Variety Channels, Digital Box Rental and two movie channels). You are considering buying satellite TV, and you figure that similar programming with satellite will cost you $55 a month. However, you will have to pay $600 up front for the appropriate satellite equipment. Assume that you can place your money in the bank at 9% annual interest, cormpounded monthly, to answer the following two questions. Hint: Best solve this with a monthly time period. a) Given the savings of the monthly satellite fee over cable, how long will it take you to repay your initial investment in the satellite equipment? (4 marks) b) How much money will you save over a period of 5 years by using satellite instead of cable? (3 marks)

Solution

9% annual interest = (9 / 12) = 0.75% interest per month.

Monthly saving from using satellite = $(80 - 55) = $25

(a)

If N be the number of months required,

$600 = $25 x (1 + 0.0075)^N

(1.0075)^N = $600 / $25 = 24

Taking logarithms (natural logarithm) at each side,

N ln (1.0075) = ln 24

N = ln 24 / ln (1.0075) = 3.1781 / 0.0075 = 424.75 (months)

(b)

Savings in 5 years (60 months) = $25 x 60 = $1,500

Present value of this saving = $1,500 / (1.0075)⁶⁰ = $1,500 / 1.5657 = $958.05