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?

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calculista calculista · Answer 1 · 2019-10-28T17:32:39+01:00

Answer:

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

Step-by-step 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

[tex]4\%=4/100=0.04[/tex]

[tex]10\%=10/100=0.10[/tex]

so

[tex]0.04(x)+0.10(21,000-x)=870[/tex]

Solve for x

[tex]0.04x+2,100-0.10x=870[/tex]

[tex]0.10x-0.04x=2,100-870[/tex]

[tex]0.06x=1,230[/tex]

[tex]x=\$20,500[/tex]

[tex]21,000-x=\$500[/tex]

therefore

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