Explanation:
First, let's calculate the amount that Eleanor would need to finance after the down payment:
$1,987.00 - $87.00 = $1,900.00
Option 1: Financing through the dealer
Finance charge:
Total amount paid - amount financed = finance charge
$169.00 x 12 months = $2,028.00
$2,028.00 - $1,900.00 = $128.00
APR:
We need to use the following formula to calculate APR:
APR = ((finance charge / amount financed) x (12 / loan term in months)) x 100
APR = (($128.00 / $1,900.00) x (12 / 12)) x 100
APR = 0.0674 x 100
APR = 6.74%
Total amount paid:
Amount financed + finance charge = total amount paid
$1,900.00 + $128.00 = $2,028.00
Option 2: Credit union loan
Finance charge:
Total amount paid - amount financed = finance charge
$114.19 x 18 months = $2,055.42
$2,055.42 - $1,900.00 = $155.42
APR:
We can use the same formula as before to calculate APR:
APR = ((finance charge / amount financed) x (12 / loan term in months)) x 100
APR = (($155.42 / $1,900.00) x (12 / 18)) x 100
APR = 0.0458 x 100
APR = 4.58%
Total amount paid:
Amount financed + finance charge = total amount paid
$1,900.00 + $155.42 = $2,055.42
The credit union loan is the better deal. Here's why:
The finance charge is lower for the credit union loan ($155.42 vs. $128.00).
The APR is also lower for the credit union loan (4.58% vs. 6.74%).
The total amount paid is higher for the credit union loan, but this is because it has a longer repayment period (18 months vs. 12 months). If we look at the total amount paid per month, the credit union loan is still the better deal ($114.19 vs. $169.00).
Therefore, Eleanor should choose the credit union loan.