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

Explanation:

Using the simple interest formula,

$I=\frac{\text{P}\times\text{n}\times\text{r}}{100}$

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,

$\begin{gathered} \text{Interest amount on federal loan + Interest amount on private loan = 700} \\ \frac{x\times1\times2}{100}+\frac{(25000-x)\times1\times3}{100}=700 \\ \frac{2x+3(25000-x)}{100}=700 \\ 2x+3(25000-x)=70000 \\ 2x+75000-3x=70000 \\ -x=-5000 \\ x=5000 \end{gathered}$

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.