Question
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)
Answers
GPT 3.5
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.
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.