Understanding Credit Quick Check
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Question
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)
To determine which plan has a lower cost of credit, we need to calculate the total amount paid for each plan.
For Plan 1:
Monthly payment = $306.91
Number of months = 5 years * 12 months/year = 60 months
Compound interest rate per period = 0.9% / 12 months = 0.075%
Using the formula for the future value of an ordinary annuity:
FV = PV * ((1 + r)^n - 1) / r
Where FV is the future value, PV is the present value (loan amount), r is the interest rate per period, and n is the number of periods.
PV = $18,000
r = 0.075% (= 0.00075)
n = 60
FV = $18,000 * ((1 + 0.00075)^60 - 1) / 0.00075 = $3,414.60
The total amount paid for Plan 1 is $3,414.60 + $18,000 = $21,414.60.
For Plan 2:
Monthly payment = $229.02
Number of months = 5 years * 12 months/year = 60 months
Compound interest rate per period = 1.9% / 12 months = 0.1583%
Using the same formula:
PV = $18,000
r = 0.1583%
n = 60
FV = $18,000 * ((1 + 0.001583)^60 - 1) / 0.001583 = $3,610.40
The total amount paid for Plan 2 is $3,610.40 + $18,000 = $21,610.40.
Comparing the two plans, Plan 1 has a lower cost of credit because it has a total amount paid of $21,414.60, while Plan 2 has a total amount paid of $21,610.40. Therefore, the lower credit cost is for Plan 1.