Question

Last year, a women's professional organization made two small-business loans totaling $28,000 to young women beginning their own businesses. The money was lent at 7% and 14% simple interest rates. If the annual income the organization received from these loans was $3,430, what was each loan amount?

Answer 1

Answer:

$7,000 at a rate of 7% and $21,000 at a rate of 14%.

Step-by-step explanation:

Let x be amount invested at 7% and y be amount invested at 14%.

We have been given that a women's professional organization made two small-business loans totaling $28,000. We can represent this information in an equation as:

$x+y=28,000...(1)$

The interest earned at 7% in one year would be $0.07x$ and interest earned at 14% in one year would be $0.14x$.

We are also told that the organization received from these loans was $3,430. We can represent this information in an equation as:

$0.07x+0.14y=3,430...(2)$

Form equation (1), we will get:

$x=28,000-y$

Upon substituting this value in equation (2), we will get:

$0.07(28,000-y)+0.14y=3,430$

$1960-0.07y+0.14y=3,430$

$1960+0.07y=3,430$

$1960-1960+0.07y=3,430-1960$

$0.07y=1470$

$\frac{0.07y}{0.07}=\frac{1470}{0.07}$

$y=21,000$

Therefore, an amount of $21,000 was invested at a rate of 14%.

$x=28,000-y$

$x=28,000-21,000$

$x=7,000$

Therefore, an amount of $7,000 was invested at a rate of 14%.