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 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.
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 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 formula for the future value of an ordinary annuity, we can calculate the total amount paid for Plan 1:
Total amount paid = Monthly payment * ((1 + monthly interest rate)^(number of months) - 1) / monthly interest rate
Monthly interest rate = 5.4% / 100 / 12 = 0.0045
Total amount paid = $361.91 * ((1 + 0.0045)^(120) - 1) / 0.0045 = $49,948.84
For Plan 2, the monthly payment is $473.49 and the repayment period is 7 years, or 7 * 12 = 84 months.
Using the same formula, we can calculate the total amount paid for Plan 2:
Monthly interest rate = 5.0% / 100 / 12 = 0.00416
Total amount paid = $473.49 * ((1 + 0.00416)^(84) - 1) / 0.00416 = $39,571.37
Therefore, Plan 2 offers the student a lower cost of credit.
The lower credit cost is $39,571.37.