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 interest received in one year total $2500, how much was loaned at 8%? How much of the 18,000 did the bank loan out at 8%?

Answer 1

The Solution:

Given that a bank loaned out $18000.

Let the amount loaned out at 8% per year be represented with x.

So that the amount loaned out at 16% per year will be $(18000-x)

Recall: By formula for simple interest ( since the simple interest is the same as compound interest if the period under consideration is 1 year), we have:

$I=\frac{\text{PRT}}{100}$

So, for the loan at 8% per year:

$\begin{gathered} I_{1_{}}=\text{ interest=?} \\ P\text{ =principal=\ x} \\ T=\text{ time =1year} \end{gathered}$

So, for the loan at 16% per year:

$\begin{gathered} I_{2_{}}=\text{ interest=?} \\ P\text{ =principal=\ (18000-x)} \\ T=\text{ time =1year} \end{gathered}$$(I_1+I_2)=\frac{8\times x\times1}{100}+\frac{(18000-x)\times16\times1}{100}$$(I_1+I_2)=\text{ \ 2500}$$2500=\frac{8x}{100}+\frac{16(18000-x)}{100}$$2500=\frac{8x+288000-16x}{100}$

Cross multiplying, we get

$250000=288000-8x$$\begin{gathered} 8x=288000-250000 \\ 8x=38000 \end{gathered}$

Dividing both sides by 8, we get

$x=\frac{38000}{8}=\text{ \ 4750}$

Thus, the amount loaned at 8% is $4750.

Therefore, the correct answer is $4750.