Question

Two investments totaling $21,000 produce an annual income of $870. One investment yields 4% per year, while the other yields 10% per year. How much is invested at each rate?

Answer 1

The amount invested at 4% is $20,500 and the amount invested at 10% is $500

Explanation:

Let

x -----> the amount invested at 4%

(21,000 -x) ----> the amount invested at 10%

we know that

The interest of the amount invested at 4% plus the interest of the amount invested at 10% must be equal to $870

`4\%=4/100=0.04`

`10\%=10/100=0.10`

so

`0.04(x)+0.10(21,000-x)=870`

Solve for x

`0.04x+2,100-0.10x=870`

`0.10x-0.04x=2,100-870`

`0.06x=1,230`

`x=\$20,500`

`21,000-x=\$500`

therefore

The amount invested at 4% is $20,500 and the amount invested at 10% is $500