Question

A total of $8000 is invested: part at 8% and the remainder at 12%. How much is invested at each rate if the annualinterest is $650?

Answer 1

Given:

`\begin{gathered} \text{Total of \$8000 was invested.} \\ \text{Total annual interest made was \$650} \end{gathered}`

The principal was invested at 8% interest rate and the remainder was invested at 12% interest rate.

We make the following representations;

`\begin{gathered} P_A=pr\text{ incipal at 8\% rate} \\ P_B=pr\text{ incipal at 12\% rate} \\ I_A=\text{interest at 8\% rate} \\ I_B=\text{interest at 12\% rate} \end{gathered}`

Recall, the formula for simple interest (I) is given by;

`\begin{gathered} I=(P* T* R)/(100) \\ \text{where;} \\ I\text{ is the interest} \\ P\text{ is the principal} \\ T\text{ is the time=yearly} \\ R\text{ is the rate} \\ \\ S\text{ ince it is annual, then T = 1} \\ \text{Hence,} \\ I=(P* R)/(100) \\ I=(PR)/(100) \end{gathered}`

Thus we get the interest made at each rates using the simple interest formula above.

Interest at 8% rate

`\begin{gathered} I=(PR)/(100) \\ I_A=(P_A*8)/(100) \\ I_A=0.08P_A \end{gathered}`

Interest at 12% rate

`\begin{gathered} I=(PR)/(100) \\ I_B=(P_B*12)/(100) \\ I_B=0.12P_B \end{gathered}`

The total interest made from both investments is $650