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 )
Plan 1 has a lower cost of credit , which is $ 1,534.55
Plan 2 has a lower cost of credit , which is $ 823.08 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 cost of each loan.
For Plan 1:
Monthly payment = $306.91
Number of payments = 5 years * 12 months/year = 60 months
Loan amount = $18,000
Using the formula for the future value of an ordinary annuity with compound interest:
FV = P * [(1 + r)^n - 1] / r
where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of payments.
FV = $306.91 * [(1 + 0.009/12)^60 - 1] / (0.009/12)
FV = $306.91 * [1.0075^60 - 1] / 0.00075
FV = $306.91 * [1.5635 - 1] / 0.00075
FV = $306.91 * 0.5635 / 0.00075
FV = $229,282.20
The total cost of this loan is the future value minus the loan amount:
Total cost = $229,282.20 - $18,000
Total cost = $211,282.20
For Plan 2:
Monthly payment = $229.02
Number of payments = 5 years * 12 months/year = 60 months
Loan amount = $18,000
Using the same formula:
FV = $229.02 * [(1 + 0.019/12)^60 - 1] / (0.019/12)
FV = $229.02 * [1.0016^60 - 1] / 0.0016
FV = $229.02 * [1.1047 - 1] / 0.0016
FV = $229.02 * 0.1047 / 0.0016
FV = $230,539.25
The total cost of this loan is the future value minus the loan amount:
Total cost = $230,539.25 - $18,000
Total cost = $212,539.25
Therefore, Plan 1 has a lower cost of credit, which is $211,282.20.
that’s wrong bot. try again
Apologies for the error in my previous response. Let's recalculate the cost of credit for each plan correctly:
For Plan 1:
Monthly payment = $306.91
Number of payments = 5 years * 12 months/year = 60 months
Loan amount = $18,000
Total amount paid = Monthly payment * Number of payments
Total amount paid = $306.91 * 60
Total amount paid = $18,414.60
Cost of credit = Total amount paid - Loan amount
Cost of credit = $18,414.60 - $18,000
Cost of credit = $414.60
For Plan 2:
Monthly payment = $229.02
Number of payments = 5 years * 12 months/year = 60 months
Loan amount = $18,000
Total amount paid = Monthly payment * Number of payments
Total amount paid = $229.02 * 60
Total amount paid = $13,741.20
Cost of credit = Total amount paid - Loan amount
Cost of credit = $13,741.20 - $18,000
Cost of credit = -$4,258.80
Since the cost of credit for Plan 2 is negative, it means that Plan 2 actually saves money compared to just paying off the loan amount. Therefore, Plan 2 has a lower cost of credit, which is $4,258.80 (or -$4,258.80 if we consider the savings).