Consider the two payment plans as shown here for an $18,000 auto loan.
Plan 1: Monthly payment of $306.91 over a period of 5 years, which corresponds to a compound interest rate of 0.9% compounded monthly.
Plan 2: Monthly payment of $229.02 over a period of 5 years, which corresponds to a compound interest rate of 1.9% compounded monthly.
Determine which plan has a lower cost of credit. Find the lower credit cost.
(1 point)
Responses
Plan 2 has a lower cost of credit, which is $823.08.
Plan 2 has a lower cost of credit, which is $823.08.
Plan 1 has a lower cost of credit, which is $1,534.55.
Plan 1 has a lower cost of credit, which is $1,534.55.
Plan 2 has a lower cost of credit, which is $414.60.
Plan 2 has a lower cost of credit, which is $414.60.
Plan 1 has a lower cost of credit, which is $414.60.
To determine which plan has a lower cost of credit, we need to calculate the total amount paid for each plan and subtract the original loan amount.
For Plan 1:
Monthly payment = $306.91
Number of months = 5 years * 12 months/year = 60 months
Compound interest rate per month = 0.9%/12 = 0.0075
Total amount paid = monthly payment * number of months = $306.91 * 60 = $18,414.60
Cost of credit = total amount paid - original loan amount = $18,414.60 - $18,000 = $414.60
For Plan 2:
Monthly payment = $229.02
Number of months = 5 years * 12 months/year = 60 months
Compound interest rate per month = 1.9%/12 = 0.1583
Total amount paid = monthly payment * number of months = $229.02 * 60 = $13,741.20
Cost of credit = total amount paid - original loan amount = $13,741.20 - $18,000 = -$4,258.80
Since the cost of credit for Plan 2 is negative, it means that the total amount paid is less than the original loan amount. Therefore, the lower cost of credit is Plan 2, which is -$4,258.80.
So the correct answer is:
Plan 2 has a lower cost of credit, which is $414.60.