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.
(1 point)
Plan offers the lower cost of credit, which is $
To determine which plan offers the student a lower cost of credit, we need to find the total amount paid for each plan and then compare them.
For Plan 1:
Monthly payment: $361.91
Number of payments: 10 years * 12 months/year = 120 months
Compound interest rate: 5.4% / 12 months = 0.45% per month
Using the formula for the future value of an ordinary annuity, we can find the total amount paid:
Total amount paid = Monthly payment * (1 - (1 + interest rate)^(-number of payments)) / interest rate
Total amount paid for Plan 1 = $361.91 * (1 - (1 + 0.45%)^(-120)) / 0.45%
For Plan 2:
Monthly payment: $473.49
Number of payments: 7 years * 12 months/year = 84 months
Compound interest rate: 5.0% / 12 months = 0.42% per month
Total amount paid for Plan 2 = $473.49 * (1 - (1 + 0.42%)^(-84)) / 0.42%
Now we can calculate the total amount paid for each plan:
Total amount paid for Plan 1 ≈ $48817.86
Total amount paid for Plan 2 ≈ $44913.56
Plan 2 offers the lower cost of credit, which is $44,913.56.