Question

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.

Explanation:

Calculate Brand F total cost

Using the Amortized Payment Calculation and Lifetime Cost Calculation knowledge points

$$
LATEXBLOCK0
$$

Calculate Brand G total cost

Using the Amortized Payment Calculation and Lifetime Cost Calculation knowledge points

$$
LATEXBLOCK1
$$

Compare the total costs

Using the Lifetime Cost Calculation knowledge point

$$
LATEXBLOCK2
$$

Using more precise intermediate values:

$$
LATEXBLOCK3
$$

Let's recalculate with standard rounding at monthly payment level:

$$
LATEXBLOCK4
$$

Brand G is cheaper by \$159.48.

Answer:

• a. Brand G will end up costing $159.48 less than Brand F. (Correct answer)
• 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.