To determine the lower cost of credit, we need to calculate the total amount paid for each payment plan.
For Plan 1, the monthly payment is $361.91 and the repayment period is 10 years, or 10 * 12 = 120 months.
Using the compound interest formula, we can calculate the total amount paid for Plan 1:
Total amount paid = Monthly payment * Number of months = $361.91 * 120 = $43,429.20
For Plan 2, the monthly payment is $473.49 and the repayment period is 7 years, or 7 * 12 = 84 months.
Using the compound interest formula, we can calculate the total amount paid for Plan 2:
Total amount paid = Monthly payment * Number of months = $473.49 * 84 = $39,823.16
Therefore, Plan 2 offers the student a lower cost of credit.
The lower credit cost is $39,823.16.