Question

A bank loaned out $26,500, part of it at the rate of 5% annual interest, and the rest at 4% annual interest. The total interest earned for both loans was $1,170.00. How much was loaned at each rate?$____ was loaned at 5% and$____ was loaned at 4%.

Answer 1

• $11,000 was loaned at 5%

,

• $15,500 was loaned at 4%.

Explanation:

• Let the amount loaned at 5% = x

Since the total amount loaned out = $26,500

• The amount loaned at 4% = $(26,500-x)

`\begin{gathered} \text{Interest}=\text{Principal}* Rate* Time \\ \text{Interest at 5\%}=0.05* x=0.05x \\ \\ \text{Interest at 4\%}=0.04(26500-x)=1060-0.04x \end{gathered}`

The total interest earned for both loans was $1,170.00.

`0.05x+(1060-0.04x)=1170`

We then solve the equation for x.

`\begin{gathered} 0.05x+1060-0.04x=1170 \\ \text{Subtract 1060 from both sides.} \\ 0.05x+1060-1060-0.04x=1170-1060 \\ 0.05x-0.04x=110 \\ 0.01x=110 \\ \text{Divide both sides by 0.01} \\ (0.01x)/(0.01)=(110)/(0.01) \\ x=11,000 \end{gathered}`

The amount loaned at 5% = $11,000

Next, we find the amount loaned at 4%.

`\begin{gathered} \text{The amount loaned at 4\%=(26,500-x)} \\ =26500-11000 \\ =\$15,500 \end{gathered}`

Thus, $11,000 was loaned at 5% and $15,500 was loaned at 4%.