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After four years in college, Josie owes $65000 in student loans. The interest rate on the federal loans is 2.4% and the rate on the private bank loans is 5%. The total interest she owes for one year was $2,730.00.What is the amount of each loan?

User Derpoliuk
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Final answer:

Josie owes a total of $65,000 in student loans; by setting up a system of linear equations based on the total loan amount and the yearly interest, we found that the federal loan amount is $20,000 and the private bank loan amount is $45,000.

Step-by-step explanation:

The student Josie wants to determine the amount of each loan she took out: one with a federal interest rate of 2.4% and the other with a private bank interest rate of 5%, given that the total interest she owes for one year is $2,730.00. To solve this, we can use a system of linear equations where:

  • x represents the amount of the federal loan.
  • y represents the amount of the private bank loan.

The total amount of loans taken is $65,000, so:

x + y = 65,000 (1)

The total interest for one year is $2,730, so the second equation using the interest rates for the loans would be:

0.024x + 0.05y = 2,730 (2)

We can solve this system of equations using substitution or elimination. For simplicity, we will use the elimination method:

Multiply equation (1) by 0.024:

0.024x + 0.024y = 1,560 (3)

Now, subtract equation (3) from equation (2):

(0.024x + 0.05y) - (0.024x + 0.024y) = 2,730 - 1,560

0.026y = 1,170

y = 1,170 / 0.026

y = 45,000

Now plug the value of y back into equation (1):

x + 45,000 = 65,000

x = 65,000 - 45,000

x = 20,000

Hence, the amount of the federal loan is $20,000 and the amount of the private bank loan is $45,000.

User Jovi
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