how much was invested at each​ rate?

Question

Things did not go quite as planned. You invested

​$18,640​,

part of it in a stock that paid​ 12% annual interest.​ However, the rest of the money suffered a​ 5% loss. If the total annual income from both investments was

​$1992​,

how much was invested at each​ rate?

Answer 1

The income from the investment at 12% interest is 0.12x, and the loss from the investment at 5% interest would be −0.05(18,640−x) (as it's a loss of 5% from the remaining amount).

The total annual income from both investments is given as $1992. Therefore, we can write the equation:

0.12x − 0.05(18,640−x) = 1992

Let's solve this equation:

0.12x − 0.05(18,640 − x) = 1992

or 0.12x − 932 + 0.05x = 1992

or 0.12x + 0.05x = 1992 + 932

or 0.17x = 2924

or x = 2924 / 0.17

or x ≈ 17,200

So, the amount invested at 12% interest (x) is approximately $17,200

Now, let's find the amount invested at 5% interest:

Amount invested at 5% = $18,640 − x = $18,640 − 17,200

Amount invested at 5% = $1,440

Therefore, approximately $17,200 was invested at 12% interest, and approximately $1,440 was invested at 5% interest.