1. Car dealers often offer \"incentives\" to lure consumers into buying a car. T
ID: 1137685 • Letter: 1
Question
1. Car dealers often offer "incentives" to lure consumers into buying a car. These incentives often take the form of various financing structures for how consumers would borrow money to pay for the car. Perhaps the most common incentive is when car dealers advertise the opportunity to choose between a "0% APR" or a "Cash Rebate" option (sometimes called a Cash Allowance). It can be difficult to determine which option is the best for you - so you'll need to do the math! Note: the term "APR'is another name for nominal interest. For car dealer incentives, the compounding period is always monthly (hence why car payments are made monthly) Consider this advertisement for a 2015 Chevrolet Malibu 2015 CHEVROLET Malibu Cash Allowance $1,500 Consumer Cash 2015 CHEVROLET Malibu Not available with finance or lease offers. Take delivery by 08 31-2015. Residency restrictions apply See dealer for details. Request A Quote Model Overview View Inventory 2015 CHEVROLET Malibu Finance Specials 0% APR for 72 months , 2015 CHEVROLET Malibu 0% APR for 72 months for qualified buyers. Monthly payment is $13 for every $1000 you finance. Example down payment 18% Some customers will not quality. Take delivery by 08-10-2015. Residency restrictions apply. See Dealer for details Request A Quate Model Overview View Inventory The key details within this advertisement are summarized in Table 1 below. Based on these details, answer the questions listed on the next page to determine which option is the best deal. Table 1: Key Details of the Chevy Malibu Financing Incentive Terms of the Incentive 0% APR Option S23,290 Manufacturer's Suggested Retail Price (MSRP) Cash Rebate Offered APR (nominal, compounded monthly) fied Term of the Loan Cash Rebate Option $23,290 $1,500 1990 72 months 0.0% 72 monthsExplanation / Answer
Answer:
a)
Monthly payment in “0% APR” = $13.80/1000*23290 = $321.40.
b)
Monthly rate = 1.9%
Monthly Installment = [P x R x (1+R)^N]/[(1+R)^N-1]
Where,
P = Principal = 23290-1500= 21790
R = Interest rate monthly = 1.9%
N = Number of months = 72
Monthly Installment = [21790 x 1.9% x (1+1.9%)^72]/[(1+1.9%)^72-1] = $421.88
Monthly payment in the “Rebate” option is $421.88
c)
Total Payment = Monthly Equal installment x 72 months
Total Amount paid in “0% APR” option = 321.40 x 72 = $23140.94
d)
Total Amount = Monthly Equal installment x 72 months
Total Amount paid in “Rebate” option = 421.88 x 72 = $30375.09
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