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Pooja Mistry

· started a discussion

· 1 Months ago

r (Question:132419.3)

s

Question:

DIRECTIONS: Study the following information carefully and answer the questions that follow:


An investor initially invests a sum of money in some securities at the start of quarter 1 of the year 1999. At the end of the quarter, the investor realizes a profit of 30%. At the beginning of quarter 2, he reinvests the amount in some speculative securities and as a result has to bear a loss of 40% at the end of that quarter. Again at the beginning of quarter 3, the investor invests his entire amount into property market and realizes a profit of 20%. He again invests the proceeds and gains 10% at the end of quarter 4 of 1999. In the first quarter of year 2000, he again invests the amount and gains 25%. Finally, he invests the amount in stock market and due to bad investment choices, has to bear loss of 30%. At the end of quarter 2 of 2000, the investor is left with Rs.2,70,270.

Assume that the investor made an investment in the quarter 3 of the year 2000. Approximately what percentage of profit does he need to earn so that he is able to obtain an amount at which he would be at a no profit no loss situation?
Options:
A) 9.91% 
B) 9.09% 
C) 10.01%
D) 11.00% 
E) 10.99%
Solution:
Let us solve the entire problem at once so that we can answer all the questions in least time.

Year

Quarter

Initial Investment Amount

Profit/Loss

Calculation

Final Amount

1999

Q1

x (assume)

+30%

x + 30% of x

130% of x

-

Q2

130% of x

-40%

130% of x – 40% of 130% of x

78% of x

-

Q3

78% of x

+20%

78% of x+ 20% of 78% of x

93.6% of x

-

Q4

93.6% of x

+10%

93.6% of x + 10% of 93.6% of x

102.96% of x

2000

Q1

102.96% of x

+25%

102.96% of x + 25% of 102.96% of x

128.7% of x

-

Q2

128.7% of x

-30%

128.7% of x - 38.61% of x

90.09% of x

 At end of quarter 2 of year 2000, the investor is left with 90.09% of the initial amount. Therefore, in order to obtain the initial amount, the investor must make a profit % as shown below: 

Let us assume that the required profit percentage is y%.

2,70,270 + y% of 2,70,270 = 3,00,000

⇒ y% of 2,70,270 = 3,00,000 - 2,70,270

⇒ y% of 2,70,270 = 29730

⇒ \(\cfrac{y}{100}\) × 270270 = 29730

⇒ y = \(\cfrac{29730}{270270}\) × 100

⇒ y = 11.0001%


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