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After four years in college, Josie owes $60000 in student loans. The interest rate on the federal loans is 2.8% and the rate on the private bank loans is 4.8%. The total interest she owes for one year was $2,760.00.What is the amount of each loan?

User Effe
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1 Answer

4 votes

Answer:

Federal student loans (F): $6,000

Private bank loans (P): $54,000

Explanation:

Let's denote the amount of the federal student loans as F and the amount of the private bank loans as P.

From the given information, we have two equations:

Josie owes a total of $60,000 in student loans:

F + P = $60,000

The total interest she owes for one year is $2,760, and we know the interest rates for both federal and private loans:

0.028F + 0.048P = $2,760

Now, we can solve this system of linear equations. We can start by solving the first equation for one of the variables and then substitute it into the second equation:

From the first equation, we can express F in terms of P:

F = $60,000 - P

Now, substitute this expression for F into the second equation:

0.028($60,000 - P) + 0.048P = $2,760

Now, let's solve for P:

0.028($60,000) - 0.028P + 0.048P = $2,760

1,680 - 0.028P + 0.048P = $2,760

Combine the like terms:

0.02P = $2,760 - $1,680

0.02P = $1,080

Now, divide by 0.02 to isolate P:

P = $1,080 / 0.02

P = $54,000

So, the amount of the private bank loans (P) is $54,000.

Now, we can find the amount of federal student loans (F) using the first equation:

F + $54,000 = $60,000

F = $60,000 - $54,000

F = $6,000

So, the amount of the federal student loans (F) is $6,000.

To summarize:

Federal student loans (F): $6,000

Private bank loans (P): $54,000

User John Culviner
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