You are interested in buying a brand-new car for a total of $22 535.60. You have the

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Question:

You are interested in buying a brand-new car for a total of $22 535.60. You have the option of paying cash for the car or you can finance the purchase through the car dealership, which offers a 4-year loan at7.45% with monthly payments. The car dealership suggests that you would be better off taking out the car loan and investing the $22 536.60 in a guaranteed investment certificate (GIC). The best interest rate on a 4-year GIC is currently4.40%. The dealership claims that you could actually earn more on your investment than you would pay in interest on the car loan. The dealership states that 48 months of interest on a 7.45% loan of $22 536.60 would be $3593.68, while the same principal invested at 4.40% per year would earn interest of $4235.80—a profit of $642.12. The reason given by the dealership for this non-intuitive result is that the 7.45% is applied to a declining balance, while the 4.40% is applied to an increasing balance.

a. Verify the figures given in the third paragraph.

b. Is the dealership correct in recommending the car loan as a better option than the cash purchase? Justify your answer