Question

After four years in college, Josie owes $25000 in student loans. The interest rate on the federal loans is 2% and the rate on the private bank loans is 3%. The total interest she owes for one year was $700.00.What is the amount of each loan?

Answer 1

Given:

The total loan amount is $ 25000.

Let x be the loan amount on a federal loan at a 2% interest rate.

Let 25000 - x be the loan amount on a private bank loan at a 3% interest rate.

The total interest for one year is I = $700.

To find: The loan amount on each loan

Step-by-step explanation:

Using the simple interest formula,

`I=\frac{\text{P}*\text{n}*\text{r}}{100}`

Where, P is the loan amount, n - years, and r - the rate of interest.

Since the sum of the interest on each loan is $ 700.

So, we can write it as,

`\begin{gathered} \text{Interest amount on federal loan + Interest amount on private loan = 700} \\ (x*1*2)/(100)+((25000-x)*1*3)/(100)=700 \\ (2x+3(25000-x))/(100)=700 \\ 2x+3(25000-x)=70000 \\ 2x+75000-3x=70000 \\ -x=-5000 \\ x=5000 \end{gathered}`

Thus, the amount on the federal loan is $5000.

The amount on the private loan is, $25000 - $5000 = $20000

Final answer:

The amount on the federal loan is $5000.

The amount on the private loan is $20000.