A student with a $33,500 student loan is offered two payment plans to repay their debt.
Plan 1: Monthly payment of $362.91 over a period of 10 years, which corresponds to a compounded interest rate of 5.4% compounded monthly.
Plan 2: Monthly payment of $473.49 over a period of 7 years, which corresponds to a compounded 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 a lower cost of credit, we need to calculate the total amount paid for each plan and compare them.
For Plan 1:
Monthly payment (PMT1) = $362.91
Number of payments (n1) = 10 years * 12 months/year = 120 payments
Compounded interest rate (r1) = 5.4% / 100% = 0.054 / 12 = 0.0045
Using the formula for the future value of an ordinary annuity:
FV1 = PMT1 * [(1 + r1)^n1 - 1] / r1
FV1 = $362.91 * [(1 + 0.0045)^120 - 1] / 0.0045
FV1 ≈ $48,524.00
The total amount paid for Plan 1 is approximately $48,524.00.
For Plan 2:
Monthly payment (PMT2) = $473.49
Number of payments (n2) = 7 years * 12 months/year = 84 payments
Compounded interest rate (r2) = 5.0% / 100% = 0.05 / 12 = 0.004167
Using the same formula:
FV2 = PMT2 * [(1 + r2)^n2 - 1] / r2
FV2 = $473.49 * [(1 + 0.004167)^84 - 1] / 0.004167
FV2 ≈ $46,712.00
The total amount paid for Plan 2 is approximately $46,712.00.
Comparing the total amounts, we can see that Plan 2 offers the student a lower cost of credit.
Therefore, Plan 2 offers the lower cost of credit, which is $46,712.00.