A car loan of $449 monthly at 3 percent annually for 48 months means you pay how much additional over the cost of $24,000 if you paid $3,500 as an initial down payment? (1 point)
To calculate the total cost of the loan, we first need to determine how much interest will be paid over the 48-month term.
The total cost of the car loan can be calculated using the formula for calculating the monthly payment on an amortizing loan:
Present Value = Payment * [(1 - (1 + r)^-n) / r]
Where:
- Present Value = Total loan amount
- Payment = Monthly payment ($449)
- r = Monthly interest rate (annual interest rate divided by 12)
- n = Total number of payments (48 months)
Given:
- Initial down payment = $3,500
- Cost of the car = $24,000
- Annual interest rate = 3%
After paying the $3,500 initial down payment, the total loan amount is $24,000 - $3,500 = $20,500.
r = 3% / 12 = 0.03 / 12 = 0.0025
Using the formula above:
$20,500 = $449 * [(1 - (1 + 0.0025)^-48) / 0.0025]
$20,500 = $449 * [(1 - 0.8181) / 0.0025]
$20,500 = $449 * 0.3181 / 0.0025
$20,500 = $449 * 127.24
$20,500 = $25,354.76
Therefore, the total cost of the loan is $25,354.76.
The amount paid on the loan over the cost of $24,000 is $25,354.76 - $24,000 = $1,354.76.
Therefore, you pay an additional $1,354.76 over the cost of $24,000 if you pay $449 monthly for 48 months at 3% annually with an initial down payment of $3,500.