surupab
An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 24 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?
(A) 92%
(B) 240%
(C) 280%
(D) 300%
(E) 380%
Since the investor bought and sold the same number (100) of shares of stock X, the percent change in his gain would be the same if he bought and sold 1 share of the stock. Therefore, let’s calculate the percent change on 1 share instead of 100 shares. Since he had to pay 2% commission on purchasing the stock (which means he actually had to pay 102% of the purchase price), his cost on one share is 6 ⅛ x 102/100 = 49/8 x 51/50. Similarly, since he had to pay 2% commission on selling the stock (which means he only received 98% of the selling price), his revenue on one share is 24 x 98/100 = 24 x 49/50.
Therefore, the ratio of the revenue to the cost of 1 share of the stock is:
(24 x 49/50)/(49/8 x 51/50)
24 x 49/50 x 8/49 x 50/51
24 x 1 x 8 x 1/51
192/51
192/51 can be approximated as 190/50 = 3.8 = 380%. That is, the revenue is approximately 380% of the cost. In other words, the profit (or gain) is approximately 280%.
Answer: C