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

Solution:

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;

$\begin{gathered} I=\frac{P\times T\times R}{100} \\ \text{where;} \\ I\text{ is the interest} \\ P\text{ is the principal} \\ T\text{ is the time=yearly} \\ R\text{ is the rate} \\ \\ S\text{ ince it is annual, then T = 1} \\ \text{Hence,} \\ I=\frac{P\times R}{100} \\ I=\frac{PR}{100} \end{gathered}$

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

Interest at 8% rate

$\begin{gathered} I=\frac{PR}{100} \\ I_A=\frac{P_A\times8}{100} \\ I_A=0.08P_A \end{gathered}$

Interest at 12% rate

$\begin{gathered} I=\frac{PR}{100} \\ I_B=\frac{P_B\times12}{100} \\ I_B=0.12P_B \end{gathered}$

The total interest made from both investments is $650

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