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. Please select the best answer from the choices provided A B C D.

Answer 1

For buying one of two brands of barbecue grills, Brand G will end up costing $159.48 less than Brand F.

What is compound interest?

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

$A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}$

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

Brand F costs $650 and will last for about fifteen years. For brand F grill the interest rate is 13. 01%, compounded monthly and five years of monthly payments. Thus, the total amount for brand F is,

$A=650\times\left(1+\dfrac{13.01}{12\times100}\right)^{12\times5}\\A=1241.37$

Brand G costs $200 and will last for about five years. For three brand G grill, the cost is,

$P=3\times200\\P=600$

For brand G grill, the interest rate is 13. 01%, compounded monthly and three years of monthly payments. Thus, the total amount for brand G is,

$A=600\times\left(1+\dfrac{13.01}{12\times100}\right)^{12\times3}\\A=884.59$

The monthly payment formula can be given as,

$M=P\times\dfrac{R/100}{1-(1+R)^{-n}}$

By this above formula, we get the total payment of brand F is 887.40 and brand G is 727.92. The difference of two is,

$d=887.40-727.92\\ d=159.48$

Thus, for buying one of two brands of barbecue grills, Brand G will end up costing $159.48 less than Brand F.

Learn more about the compound interest here;

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