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 which plan offers the student a lower cost of credit, we need to calculate the total amount paid for each plan.
For Plan 1, the total amount paid can be calculated using the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
where FV is the future value, P is the monthly payment, r is the interest rate per period, and n is the number of periods.
Using the given values for Plan 1:
P = $361.91
r = 5.4% = 0.054/12 = 0.0045 (monthly interest rate)
n = 10 years * 12 months/year = 120 months
FV = 361.91 * ((1 + 0.0045)^120 - 1) / 0.0045
FV ≈ $43,429.25
So the total amount paid for Plan 1 is approximately $43,429.25.
For Plan 2, we can use the same formula:
P = $473.49
r = 5.0% = 0.05/12 = 0.004167 (monthly interest rate)
n = 7 years * 12 months/year = 84 months
FV = 473.49 * ((1 + 0.004167)^84 - 1) / 0.004167
FV ≈ $46,022.26
So the total amount paid for Plan 2 is approximately $46,022.26.
Since Plan 1 has a lower total amount paid, it offers the student a lower cost of credit.
To find the lower credit cost, we subtract the initial loan amount from the total amount paid for Plan 1:
Lower credit cost = Total amount paid - Loan amount
Lower credit cost = $43,429.25 - $33,500
Lower credit cost ≈ $9,929.25
Therefore, the lower credit cost for Plan 1 is approximately $9,929.25.