Question

A bank loaned out $18,000, part of it at the rate of 8%per year and the rest at 16% per year. If the interestreceived in one year totaled $2500 how much wasloaned at 8%?How much of the $18000 did the bank loan out at 8%?

Answer 1

The total loan was $18,000.

Let's set x as the amount that was loaned at 8% (0.08 in decimal form)

Thus, the amount that was loaned at 16% (0.16 in decimal form) is (18,000-x).

If in one year the total interest received was $2500, we can state the next equation:

`0.08x+0.16(18,000-x)=2500`

Apply the distributive property and solve for x:

`\begin{gathered} 0.08x+0.16\cdot18,000-0.16\cdot x=2500 \\ 0.08x+2880-0.16x=2500 \\ -0.08x+2880=2500 \\ \text{Subtract 2880 from both sides} \\ -0.08x+2880-2880=2500-2880 \\ -0.08x=-380 \\ \text{Divide both sides by -0.08} \\ (-0.08x)/(-0.08)=(-380)/(-0.08) \\ \text{Simplify} \\ x=4750 \end{gathered}`

So, of the $18,000 the bank loaned $4750 at 8%.