Question

You wish to purchase a new 2020 Ford Mustang listed at $33000. The deal is offering incentives to new car buyers. There are two choices: A) $1600 cash back on a new Mustang with 1.7% financing for 69 months. B) 0% financing for 69 months. Assume that all compounding and repayment is continuous. Once you determine which offer is ultimately less expensive, en- ter the difference (i.e. how much cheaper is one financing option over the other). Round your answer to the nearest dollar.

Answer 1

Amount to be paid after 69 months at 1.7% = P * ( 1 + r/n ) ^ nt   ( here, p=principal, r=rate, n=annual no of compoundings, t = time period )

= 33000 * (1 + 0.017 / 12 ) ^ 69

= 33000 * (1.0014166666666 ^ 69 )

= 33000 * 1.1026108039476

= 36386

Net payment after cash back = 36386 - 1600 = 34786

On the other hand, if we choose 2nd option with 0 % finance for 69 months, Total payment made will be 33000 only

Thus, Option 2 for 0% finance is definately less expensive.

Total differenc or benefit = 34786 - 33000 = 1786