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.)

a. Brand G will end up costing $159.48 less than Brand F.

b. Brand G will end up costing $50.00 less than Brand F.

c. Brand F will end up costing $134.28 less than Brand G.

d. Brand F will end up costing $91.08 less than Brand G.

Question

Mathematics

Natalia Reid

25 December, 06:11

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.)

a. Brand G will end up costing $159.48 less than Brand F.

b. Brand G will end up costing $50.00 less than Brand F.

c. Brand F will end up costing $134.28 less than Brand G.

d. Brand F will end up costing $91.08 less than Brand G.

+1

Answers (1)

Know the Answer?

Emmy Mejia · Answer 1

Formula would be: M = P * (J / (1 - (1 + J) ^ - N)).

M: monthly payment

P: principal or amount of loan

J: monthly interest; annual interest divided by 100, then divided by 12.

N: number of months of amortization, determined by length in years of loan.

Then substitute, so we choose brand F and G

Brand F

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

Brand G

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

total price of 726.84

So Brand G is cheaper by 161.16