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 student a lower cost of credit, we need to calculate the total amount paid for each plan.
For Plan 1:
Monthly payment: $361.91
Number of months: 10 years * 12 months/year = 120 months
Compound interest rate: 5.4% / 12 = 0.45% per month
Using the formula for compound interest:
A = P(1 + r)^n
where A is the final amount, P is the principal amount, r is the interest rate, and n is the number of periods
Plugging in the values:
A = 361.91(1 + 0.0045)^120
A = 361.91 * 1.738198
A = 628.8280258
The total amount paid for Plan 1 is 120 * 361.91 = $43,429.20
For Plan 2:
Monthly payment: $473.49
Number of months: 7 years * 12 months/year = 84 months
Compound interest rate: 5.0% / 12 = 0.416667% per month
Using the formula for compound interest:
A = P(1 + r)^n
Plugging in the values:
A = 473.49(1 + 0.00416667)^84
A = 473.49 * 1.425676
A = 674.7509172
The total amount paid for Plan 2 is 84 * 473.49 = $39,796.16
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 $39,796.16 - $33,500 = $6,296.16.