Question

You invest a total of $200,000 for one year, part at 9% interest and part at 8% interest. The total annual interest is $17,200. How much wasinvested at each interest rate?

Answer 1

Let the money(principal) invested at 9% be x and

Let the money(principal) invested at 8% be y

Using the simple interest formula

`I=(PRT)/(100)`

We have

`\begin{gathered} I_x\text{ that is interest at principal x becomes } \\ I_x=(x*9*1)/(100) \\ I_x=0.09x \end{gathered}`

And

`\begin{gathered} I_y\text{ that is interest at principal y becomes } \\ I_y=(y*8*1)/(100) \\ I_y=0.08y \\ \text{But y = 200,000 - }x \\ \text{Hence } \\ I_y=0.08(\text{200,000 - }x) \\ I_y=16000-0.08x \end{gathered}`

Combining, we have

`\begin{gathered} 0.09x+16000-0.08x=17,200 \\ 0.09x-0.08x=17,200-16,000 \\ 0.01x=1200 \\ x=(1200)/(0.01) \\ x=120,000\text{ dollars } \end{gathered}`

Then,

`\begin{gathered} y=200,000-x \\ y=200,000-120,000 \\ y=80,000\text{ dollars } \end{gathered}`

Hence, the answer is 9% interest rate was $120,000 and 8% interest rate was $80,000