Problema Solution
You are considering buying one of two brands of barbecue grills. Brand F costs $650 and will last for about fifteen years. Brand G costs $200 and will last for about five years, so you will need to buy three of them over the years to equal one Brand F grill. In either case, you plan to pay for the grill with your credit card, which has an interest rate of 13.01%, compounded monthly. You will pay off a Brand F grill in five years of monthly payments, and you will pay off a Brand G grill in three years of monthly payments. Assuming that you have no other purchases on your credit card, over a fifteen-year period, which kind of grill will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.)
Answer provided by our tutors
M = P * ( J / (1 - (1 + J)^ -N)).
M = monthly payment
P = principal or amount of loan
J = monthly interest (annual interest as a decimal divided by 12)
N = number of months of amortization, determined by length in years of loan
Applying this to Brand F:
P = $650
J = 0.1301/12 = 0.01084166666
N = 5*12 months
M = 650 * (0.01084166666 / (1 - (1 + 0.01084166666)^(-(5 * 12))))
........
........
M = 14.79
And over the 5 years that is 14.79 * 5 * 12 = $887.4
Applying this to Brand G:
P = $200
J = 0.1301/12 = 0.01084166666
N = 5*12 months
M = 200 * (0.01084166666 / (1 - (1 + 0.01084166666)^(-(3 * 12))))
........
........
M = 6.73
And over the 3 years that is 6.73 * 3 * 12 = $242.28
Doing this three times gives a total price of 3*242.28 = $726.84
$726.84 < $887.4
So Brand G is cheaper by 887 - 726.84 = $161.16.