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.
Plan ___ offers the lower cost of credit, which is $
To determine which plan offers the student a lower cost of credit, we need to calculate the total amount paid for each plan and compare them.
For Plan 1:
Monthly payment = $361.91
Number of months = 10 years * 12 months/year = 120 months
Interest rate per month = 5.4% / 100 / 12 = 0.0045
The total amount paid can be calculated using the formula for the future value of an ordinary annuity:
FV = PMT * ((1 + r)^n - 1) / r
Where FV is the future value (total amount paid), PMT is the monthly payment, r is the interest rate per period, and n is the number of periods.
Using this formula:
FV1 = $361.91 * ((1 + 0.0045)^120 - 1) / 0.0045
FV1 ≈ $46,032.25
For Plan 2:
Monthly payment = $473.49
Number of months = 7 years * 12 months/year = 84 months
Interest rate per month = 5.0% / 100 / 12 = 0.0042
Using the same formula:
FV2 = $473.49 * ((1 + 0.0042)^84 - 1) / 0.0042
FV2 ≈ $39,799.40
Therefore, Plan 2 offers the student a lower cost of credit.
The lower cost of credit is $39,799.40.