Question

Derek plans to buy a $33,277.00 car. The dealership offers zero percent financing for 56.00 months with the first payment due at signing (today). Derek would be willing to pay for the car in full today if the dealership offers him $____ cash back. He can borrow money from his bank at an interest rate of 5.80%.

Submit

Answer format: Currency: Round to: 2 decimal places.

Answer 1

Cost of car = $33,277

Derek has 2 options to finace cost of this car.

Option 1

Use the zero percent financing option provided by dealership.

This means he has to pay $33,277 ($594.23 for 56 months)

Option 2

Borrow money from bank at 5.8% interest rate.

This means he has to pay to bank $1930.07 ($33,277*5.8%)

So in Option 1 Derek has to pay a total of  $33,277.

And in Option 2 Derek has to pay a total of $33,277 + $1930.07 (as interest).

If the dealership offers $1930.07 as cash back to him on paying full amount today, his financing cost becomes same ($33,277) for both options. Hence the anser is $1930.07.

Derek would be willing to pay for the car in full today if the dealership offers him $1930.07 cash back.

Assumptions used

It is assumed that bank's interest rate 5.8% is a one off payment on borrowing money.