Question 14 of 15 Aliyah earned a $8000 bonus from her sales job for exceeding h

Question

Question 14 of 15 Aliyah earned a $8000 bonus from her sales job for exceeding her sales goals. After paying taxes at a 25% rate, she invested the remaining money in two stocks. One stock returned the| equivalent of 12% simple interest after l yr, and the other returned 7% at the end of 1 vr. If her,investments returned S596.30 (excluding commissions) how much did she invest in each stock? Round to the nearest dollar, if necessary. Part 1 The amount invested in the stock retuning 12% is S Part 2 The amount invested in the stock returning 7% is

Explanation / Answer

Aliyah pays taxes @ 25 % of $ 8000 i.e. $ 2000. After paying the taxes, the amount that remains with her is $ 80000-$ 2000 = $ 6000. Let Aliyah invest $ x in the stock returning equivalent of 12 % interest. Then, the amount invested by Aliyah in the stock returning equivalent of 7 % interest is $ 6000 – x. Now, the interest on $ x for 1 year @ 12 % is x* 12/100 = 0.12x and the interest on $ 6000-x for 1 year @ 7 % is (6000-x)*7/100 = 420- 0.07x. Since the aggregate return on Aliyah’s investments is $ 596.30, we have 0.12x + 420 -0.07x = 596.30 or, 0.05x = 596.30-420 = 176.30 so that x = 176.30/0.05 = 3526.

Thus,the amount invested in the stock returning 12 % is $ 3526.

Also, the amount invested in the stock returning 7 % is $ 6000- $ 3526 = $ 2474.

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