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.

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,[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]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,[tex]A=650\times\left(1+\dfrac{13.01}{12\times100}\right)^{12\times5}\\A=1241.37[/tex]Brand G costs $200 and will last for about five years. For three brand G grill, the cost is,[tex]P=3\times200\\P=600[/tex]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,[tex]A=600\times\left(1+\dfrac{13.01}{12\times100}\right)^{12\times3}\\A=884.59[/tex]The monthly payment formula can be given as,[tex]M=P\times\dfrac{R/100}{1-(1+R)^{-n}}[/tex]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,[tex]d=887.40-727.92\\ d=159.48[/tex]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;