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

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

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`

`(0.07y)/(0.07)=(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%.