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Penni Saver plans to invest $10,000, part of it in utility bonds paying 9% per year and the rest in a savings account paying 6% per year. How much should be allocated to each investment if the yearly income from the two investments is to be the same?

$4,000 in utility bonds and $6,000 in a savings account

$3,000 in utility bonds and $7,000 in a savings account

$3,500 in utility bonds and $6,500 in a savings account

$2,500 in utility bonds and $7,500 in a savings account

$4,500 in utility bonds and $5,500 in a savings account

Respuesta :

Answer:

The correct option is 1.

Step-by-step explanation:

Let the amount invested in utility bound be x. So, the amount invested in saving account is (10000-x).

It is given that the yearly income from the two investments is same.

[tex]\text{9\% of x}=\text{6\% of (10000-x)}[/tex]

[tex]\frac{9}{100}\times x=\frac{6}{100}\times (10000-x)[/tex]

[tex]\frac{9x}{100}=600-\frac{6x}{100}[/tex]

[tex]\frac{9x}{100}+\frac{6x}{100}=600[/tex]

[tex]\frac{15x}{100}=600[/tex]

[tex]15x=60000[/tex]

[tex]x=4000[/tex]

The amount invested in utility bound is $4000.

[tex]10000-x=10000-4000=6000[/tex]

The amount invested in saving account is $6000.

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