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 over the life of the loan for each plan and compare them.
For Plan 1:
The monthly payment is $361.91 for 10 years, which is a total of 10 * 12 = <<10*12=120>>120 payments.
The compound interest rate is 5.4% per year, compounded monthly.
The loan amount is $33,500.
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 monthly interest rate, and n is the number of payments.
The future value of the loan for Plan 1 is:
FV1 = $361.91 * ((1 + 5.4%/12)^(10*12) - 1) / (5.4%/12) = $48,237.97
The total amount paid over the life of the loan for Plan 1 is:
Total1 = $361.91 * 120 = $43,429.20
For Plan 2:
The monthly payment is $473.49 for 7 years, which is a total of 7 * 12 = <<7*12=84>>84 payments.
The compound interest rate is 5.0% per year, compounded monthly.
The loan amount is $33,500.
Using the same formula:
The future value of the loan for Plan 2 is:
FV2 = $473.49 * ((1 + 5.0%/12)^(7*12) - 1) / (5.0%/12) = $43,388.81
The total amount paid over the life of the loan for Plan 2 is:
Total2 = $473.49 * 84 = $39,751.16
Comparing the total amounts paid, we can see that Plan 2 offers the student a lower cost of credit.
The lower cost of credit is:
Total2 - Total1 = $39,751.16 - $43,429.20 = -$3,678.04
Rounding to two decimal places, the lower credit cost is -$3,678.04.