question 7\na bank loaned out $21,500, part of it at the rate of 10% annual interest, and the rest at 2%…

question 7\na bank loaned out $21,500, part of it at the rate of 10% annual interest, and the rest at 2% annual interest. the total interest earned for both loans was $1,270.00. how much was loaned at each rate?\n$ was loaned at 10% and\n$ was loaned at 2%.\nquestion help: video message instructor post to forum

question 7\na bank loaned out $21,500, part of it at the rate of 10% annual interest, and the rest at 2% annual interest. the total interest earned for both loans was $1,270.00. how much was loaned at each rate?\n$ was loaned at 10% and\n$ was loaned at 2%.\nquestion help: video message instructor post to forum

Answer

Explanation:

Step1: Let the amount loaned at 10% be $x$.

Then the amount loaned at 2% is $(21500 - x)$.

Step2: Calculate the interest from each loan.

The interest from the 10% - loan is $0.1x$, and the interest from the 2% - loan is $0.02(21500 - x)$.

Step3: Set up the equation based on the total - interest.

$0.1x+0.02(21500 - x)=1270$.

Step4: Expand and simplify the equation.

$0.1x + 430-0.02x=1270$. Combining like - terms gives $0.1x-0.02x=1270 - 430$. $0.08x=840$.

Step5: Solve for $x$.

$x=\frac{840}{0.08}=10500$.

Step6: Find the amount loaned at 2%.

The amount loaned at 2% is $21500 - 10500 = 11000$.

Answer:

$10500$ was loaned at 10% and $11000$ was loaned at 2%.