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.
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)
1 answer