Consider the two payment plans as shown for a $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.
a Plan 1 has a lower cost of credit, which is $1,534.55
b Plan 2 has a lower cost of credit, which is $823.08
c Plan 2 has a lower cost of credit, which is $414.60
d 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 of $18,000 from that total.
For Plan 1:
Monthly payment = $306.91
Number of payments = 5 years * 12 months = 60 months
Compound interest rate = 0.9% / 12 = 0.0075
Total amount paid = Monthly payment * Number of payments = $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 payments = 5 years * 12 months = 60 months
Compound interest rate = 1.9% / 12 = 0.0158
Total amount paid = Monthly payment * Number of payments = $229.02 * 60 = $13,741.20
Cost of credit = Total amount paid - Original loan amount = $13,741.20 - $18,000 = -$4,258.80
Since Plan 2's cost of credit is negative, it means that the total amount paid is less than the original loan amount. This indicates that Plan 2 has a lower cost of credit. Therefore, the correct answer is:
c Plan 2 has a lower cost of credit, which is $414.60