To determine which plan offers the student a lower cost of credit, we need to calculate the total payments made under each plan and compare them.
For Plan 1, the monthly payment is $361.91 and it stretches over a period of 10 years, or 10 x 12 months = 120 months. The total payment made under this plan is therefore 120 x $361.91 = $43,429.20.
For Plan 2, the monthly payment is $473.49 and it stretches over a period of 7 years, or 7 x 12 months = 84 months. The total payment made under this plan is therefore 84 x $473.49 = $39,757.16.
To find the cost of credit for both plans, we subtract the original loan amount of $33,350 from the total payments made.
For Plan 1, the cost of credit is $43,429.20 - $33,350 = $10,079.20.
For Plan 2, the cost of credit is $39,757.16 - $33,350 = $6,407.16.
Therefore, the lower cost of credit is $6,407.16, which corresponds to Plan 2.