Question

You invested 21,020 part of it in a stock that paid 12% annual interest. The rest suffered a 5% loss. If the total annual income from both investments was 1890 how much was invested at each rate?

Answer 1

The total investment was 21,020. Let:

x = part invested at 12% annual interest

The other part suffered a 5% loss. Since both parts must add up to 21,020, then:

21,020 - x = part that suffered a 5% loss.

The first part earned an interest:

$I_1=0.12x$

The second part lost interest:

$I_2=-0.05(21,020-x)$

The sum of both interests is I1 + I2 and was 1,890, thus:

$0.12x-0.05(21,020-x)=1,890$

Operating:

$\begin{gathered} 0.12x-1051+0.05x=1,890 \\ \\ 0.17x=1,890+1,051=2,941 \end{gathered}$

Dividing by 0.17:

$x=\frac{2,941}{0.17}=17,300$

Thus, $17,300 was invested at 12% annual interest and 21,020 - 17,300 = $3,720 were invested at a 5% loss.

Answer: $17,300 and $3,720.