Question

When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?

Answer 1

Amount of loan from federal : $ 29,000

Amount of loan from private bank : $ 14,000

Explanation:

We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.

If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -

x + y = 43,000

At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -

0.045x + 0.02y = 1585

Let's solve the following system for x and y, the amount of each loan,

`\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}` ( Substitute x = 43000 - y )

`0.045\left(43000-y\right)+0.02y=1585` ( Simplify )

`1935-0.025y=1585`,

`1935000-25y=1585000`,

`-25y=-350000`,

`y=14000`,

`x=29000`

Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.

Answer 2

federal loans = $29,000

private loans = $14,000

Explanation:

x + y = 43000

.045x + .02y = 1585

x = 29,000

y = 14,000