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)
Plan offers the lower cost of credit, which is $
To determine which plan offers the lower cost of credit, we need to calculate the total amount paid under each plan and then subtract the initial loan amount of $33,500 to find the cost of credit.
For Plan 1:
We have a monthly payment of $361.91 for a period of 10 years, which is equivalent to 120 monthly payments.
Using the compound interest formula A = P(1 + r/n)^(nt), where:
A = the total amount paid
P = the monthly payment
r = the annual interest rate (5.4% or 0.054)
n = the number of times interest is compounded per year (monthly, so 12)
t = the number of years (10)
Substituting the given values, we get:
A = 361.91(1 + 0.054/12)^(12*10)
A ≈ 361.91(1 + 0.0045)^(120)
A ≈ 361.91(1.0045)^120
A ≈ 361.91(1.64748)
A ≈ $59,588.90
The cost of credit under Plan 1 is $59,588.90 - $33,500 = $26,088.90.
For Plan 2:
We have a monthly payment of $473.49 for a period of 7 years, which is equivalent to 84 monthly payments.
Using the same compound interest formula, we get:
A = 473.49(1 + 0.05/12)^(12*7)
A ≈ 473.49(1 + 0.0041667)^(84)
A ≈ 473.49(1.0041667)^84
A ≈ $46,647.09
The cost of credit under Plan 2 is $46,647.09 - $33,500 = $13,147.09.
Comparing the two costs of credit, we can see that Plan 2 offers the lower cost, which is $13,147.09.