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)
To determine the lower cost of credit, we need to calculate the total amount paid for each payment plan and then compare the two amounts.
For Plan 1:
Monthly payment = $361.91
Number of months = 10 years * 12 months/year = 120 months
Using the compound interest formula, we can calculate the total amount paid for Plan 1 as follows:
PV = 33,500 (the initial loan amount)
n = 120 (the number of monthly payments)
r = 5.4%/12 = 0.45% (the monthly interest rate)
Total amount paid for Plan 1 = PV * [(1 + r)^n - 1] / r
= 33,500 * [(1 + 0.0045)^120 - 1] / 0.0045
≈ 43,429.78
For Plan 2:
Monthly payment = $473.49
Number of months = 7 years * 12 months/year = 84 months
Using the same compound interest formula, we can calculate the total amount paid for Plan 2 as follows:
PV = 33,500 (the initial loan amount)
n = 84 (the number of monthly payments)
r = 5.0%/12 = 0.4167% (the monthly interest rate)
Total amount paid for Plan 2 = PV * [(1 + r)^n - 1] / r
= 33,500 * [(1 + 0.004167)^84 - 1] / 0.004167
≈ 38,218.85
Comparing the two amounts, we can see that the total amount paid for Plan 2 is lower than Plan 1.
Therefore, Plan 2 offers the student a lower cost of credit. The lower credit cost is $38,218.85.