You are purchasing a car for $12,465.00 plus 5.65% sales tax. You make a $1,300.00 down payment and have a fair credit score. If you improved your credit score to good and paid $1,500 on your purchase, how much interest could you save in the first month?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
$25.69
$21.74
$13.25
$14.68
To calculate the interest savings in the first month, we need to determine the interest rate for the original credit score and the improved credit score.
For the original credit score (fair), the APR is 6.40% for secured credit and 7.25% for unsecured credit.
For the improved credit score (good), the APR is 5.00% for secured credit and 5.90% for unsecured credit.
Next, we need to calculate the total amount financed after the down payment for both scenarios:
Original credit score:
Total purchase price = $12,465.00 + (5.65% * $12,465.00) = $13,136.42
Amount financed = Total purchase price - down payment = $13,136.42 - $1,300.00 = $11,836.42
Improved credit score:
Amount financed = Total purchase price - down payment = $13,136.42 - $1,500.00 = $11,636.42
Now, we can calculate the interest savings in the first month by finding the difference between the interest payments for both scenarios:
Original credit score:
Interest payment in the first month = (6.40% / 12) * $11,836.42 = $62.92
Improved credit score:
Interest payment in the first month = (5.00% / 12) * $11,636.42 = $48.33
Therefore, the interest savings in the first month would be:
Interest savings = Interest payment with original credit score - Interest payment with improved credit score
= $62.92 - $48.33 = $14.59
Rounded to the nearest cent, the interest savings in the first month would be $14.59.
To calculate the amount of interest that can be saved in the first month, we need to compare the interest rates for fair credit and good credit.
For the given purchase amount of $12,465.00, the sales tax of 5.65% would be calculated as follows:
Sales Tax = (Purchase Price) x (Sales Tax Rate)
Sales Tax = $12,465.00 x 5.65%
Sales Tax = $703.42
Therefore, the total cost of the car including sales tax would be:
Total Cost = Purchase Price + Sales Tax
Total Cost = $12,465.00 + $703.42
Total Cost = $13,168.42
With a fair credit score, a $1,300.00 down payment is made, leaving an unpaid amount of:
Unpaid Amount = Total Cost - Down Payment
Unpaid Amount = $13,168.42 - $1,300.00
Unpaid Amount = $11,868.42
With an improved credit score to good, a $1,500.00 down payment is made, leaving an unpaid amount of:
Unpaid Amount = Total Cost - Down Payment
Unpaid Amount = $13,168.42 - $1,500.00
Unpaid Amount = $11,668.42
The interest saved can be calculated using the difference in unpaid amounts and the difference in interest rates for fair credit and good credit:
Interest Saved = (Unpaid Amount with Fair Credit x Interest Rate for Fair Credit) - (Unpaid Amount with Good Credit x Interest Rate for Good Credit)
Interest Saved = ($11,868.42 x 6.4%) - ($11,668.42 x 5%)
Interest Saved = $759.00 - $583.42
Interest Saved = $175.58
Therefore, the amount of interest that could be saved in the first month with an improved credit score and a $1,500.00 down payment is $175.58.
$12,465.00 plus 5.65% = 13,169.27
less 1300 down leaves 11,869.27
1st month's interest on that is $55.88
Now check the other interest rates and compare.