Question

Eliza is looking at purchasing a $33,000 new SUV at a dealership with a $2,000 down payment. - Sellwell Cars (the dealership) has offered Eliza two choices:

Option 1) A $2,500 non-cash rebate (amount subtracted from the $33,000 price) and Vicki needs to finance her new vehicle somewhere else. Eliza has done her research and knows that she can get a 6%, 4-year loan from her credit union.
Option 2) A dealer loan (no $2,500 rebate) with a rate of 2% over 4 years

Answer 1

Option 1 will have a monthly payment of approximately $688.60, while Option 2 will have a slightly lower monthly payment of approximately $687.87.

Step-by-step explanation:

To compare Option 1 and Option 2, let's calculate the total cost of each choice over 4 years.

Option 1: With a final answer in two line

explantion in 300 words$2,500 non-cash rebate, Eliza will need to finance $30,500 ($33,000 - $2,500). Using her credit union loan at 6% interest, she can calculate the monthly payment using the formula for a loan:

1. Convert the annual interest rate to a monthly rate: 6% ÷ 12 = 0.5%
2. Divide the loan amount by the present value annuity factor based on the interest rate and loan term. Using a loan term of 4 years and a monthly rate of 0.5%, the present value annuity factor is 44.3195.
3. Divide the result by the present value annuity factor to find the monthly payment: $30,500 ÷ 44.3195 ≈ $688.60.
   

Therefore, Option 1 will have a monthly payment of approximately $688.60.

Option 2: With no rebate, Eliza will finance the full $33,000. Using the dealer loan at 2% interest, she can calculate the monthly payment in the same way:

1. Convert the annual interest rate to a monthly rate: 2% ÷ 12 = 0.167%
2. Divide the loan amount by the present value annuity factor based on the interest rate and loan term. Using a loan term of 4 years and a monthly rate of 0.167%, the present value annuity factor is 47.9837.
3. Divide the result by the present value annuity factor to find the monthly payment: $33,000 ÷ 47.9837 ≈ $687.87.
   

Therefore, Option 2 will have a slightly lower monthly payment of approximately $687.87.