A student with a $33,500 student loan is offered two payment plans to repay their debt. Plan 1: Monthly payment of $361.91 over a period of 10 years, which corresponds to a compound interest rate of 5.4% compounded monthly. Plan 2: Monthly payment of $473.49 over a period of 7 years, which corresponds to a compound interest rate of 5.0% compounded monthly. Determine which plan offers the student a lower cost of credit. Find the lower credit cost. Round the answer to two decimal places as needed.
To determine which plan offers the student a lower cost of credit, we need to calculate the total amount paid for each plan.
For Plan 1, the total amount paid can be calculated using the formula:
Total Amount Paid = Monthly Payment * Number of Months
The number of months for Plan 1 is 10 years * 12 months/year = 120 months.
So, Total Amount Paid for Plan 1 = $361.91 * 120 = $43,429.20
For Plan 2, the total amount paid can also be calculated using the formula:
Total Amount Paid = Monthly Payment * Number of Months
The number of months for Plan 2 is 7 years * 12 months/year = 84 months.
So, Total Amount Paid for Plan 2 = $473.49 * 84 = $39,817.16
Therefore, Plan 2 offers the student a lower cost of credit.
To find the lower credit cost, we need to subtract the original loan amount from the total amount paid for each plan.
For Plan 1, the lower credit cost can be calculated as:
Lower Credit Cost for Plan 1 = Total Amount Paid for Plan 1 - Loan Amount
= $43,429.20 - $33,500 = $9,929.20
For Plan 2, the lower credit cost can be calculated as:
Lower Credit Cost for Plan 2 = Total Amount Paid for Plan 2 - Loan Amount
= $39,817.16 - $33,500 = $6,317.16
Therefore, the lower credit cost is $6,317.16.