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A bank loaned $20,000 part of the rate was at 8% and the rest at 13% per year. If the interest in one year totaled $2,000, how much was loaned at 8%?

Respuesta :

SOLUTION:

Step 1:

In this question, we are given the following:

A bank loaned $20,000 part of the rate was at 8% and the rest at 13% per year. If the interest in one year totaled $2,000, how much was loaned at 8%?

Step 2:

Let x represents the amount loaned at 8% .

Then the interest earned is given by:

[tex]\begin{gathered} 0.08x\text{ + 0.13( 2000}0\text{ - x) =2000} \\ 0.08x\text{ + 2600 -0. 13 x = 2000} \\ 0.08\text{ x -0. }13\text{ x = 2000 -26}00 \\ -0.05x\text{ = }-600 \\ \text{Divide both sides by -0.05, we have that:} \\ \text{x =}\frac{-600}{-0.05} \\ x\text{ = 12000} \end{gathered}[/tex]

CONCLUSION:

$ 12, 000 was loaned at 8 %

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