Question

A bank loaned out $17,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest in one year totaled 2,000, how much was loaned at 8%?

Answer 1

`\$10,600`

Step-by-step explanation

Let the amount loaned at 8% be x.

We have that interest of 8% on x plus interest of 18% on the rest of the money yields an interest of $2,000.

Simple interest can be gotten by applying the formula:

`I=(P\cdot R\cdot T)/(100)`

where P = principal, R = rate, T = time

So, we can write that:

`(x\cdot0.08\cdot1)+(\lbrack17000-x\rbrack\cdot0.18\cdot1)=2000`

Simplify the equation above and solve for x:

`\begin{gathered} 0.08x+0.18(17000-x)=2000 \\ \Rightarrow0.08x+3060-0.18x=2000 \\ -0.1x=2000-3060 \\ -0.1x=-1060 \\ x=(-1060)/(-0.1) \\ x=\$10,600 \end{gathered}`

Therefore, the amount loaned at 8% is $10,600.