Paul paid $663 for a new freezer. He paid for the freezer with his credit card, which has an interest rate of 15.28% compounded monthly, and made monthly payments for five years until the freezer was paid off. He kept the freezer for seven years, and it used an average of $2.14 of electricity per week. Paul made no other purchases or payments with his credit card until the freezer was paid off. Between the interest and the electricity, which component of the lifetime cost of the freezer was greater, and how much greater was it? (Round all dollar values to the nearest cent

Question

Mathematics

Rayna Hunt

28 February, 20:30

Paul paid $663 for a new freezer. He paid for the freezer with his credit card, which has an interest rate of 15.28% compounded monthly, and made monthly payments for five years until the freezer was paid off. He kept the freezer for seven years, and it used an average of $2.14 of electricity per week. Paul made no other purchases or payments with his credit card until the freezer was paid off. Between the interest and the electricity, which component of the lifetime cost of the freezer was greater, and how much greater was it? (Round all dollar values to the nearest cent

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Amirah King · Answer 1

The present value of an annuity is given by PV = P (1 - (1 + r) ^n) / r; where P is the periodic (monthly) payment, r is the rate, and n is the number of periods.

Here, PV = $663, r = 15.28%/12 = 0.01273, n = 12 x 5 = 60.

663 = P (1 - (1 + 0.01273) ^-60) / 0.01273

P = 663 x 0.01273 / (1 - (1 + 0.01273) ^-60) = 8.4422/0.5319 = $15.87

Total payment = $15.87 x 60 months = $952.20

Interest = $952.20 - $663 = $289.20

Electricity charge = $2.14 x 52 x 7 = $778.96

The electricity charge is greater than the interest by $778.96 - $289.20 = $489.76