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..
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 monthly payment is $361.91, and the loan period is 10 years or 120 months. The compound interest rate is 5.4% compounded monthly.
Using the compound interest formula, we can calculate the loan amount, A:
A = P(1 + r/n)^(nt)
Where:
P = principal loan amount
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, P = $33,500, r = 0.054 (5.4% as a decimal), n = 12 (compounded monthly), and t = 10.
A = $33,500(1 + 0.054/12)^(12*10)
A ≈ $61,415.12
The total amount paid is the monthly payment multiplied by the number of months:
Total amount paid = Monthly payment * Number of months
Total amount paid = $361.91 * 120
Total amount paid ≈ $43,429.20
For Plan 2:
The monthly payment is $473.49, and the loan period is 7 years or 84 months. The compound interest rate is 5.0% compounded monthly.
Using the compound interest formula, we can calculate the loan amount, A:
A = P(1 + r/n)^(nt)
Where:
P = principal loan amount
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, P = $33,500, r = 0.05 (5.0% as a decimal), n = 12 (compounded monthly), and t = 7.
A = $33,500(1 + 0.05/12)^(12*7)
A ≈ $46,144.47
The total amount paid is the monthly payment multiplied by the number of months:
Total amount paid = Monthly payment * Number of months
Total amount paid = $473.49 * 84
Total amount paid ≈ $39,822.84
Therefore, Plan 2 offers the student a lower cost of credit. The lower credit cost is approximately $39,822.84.