An investment has been growing at a fixed annual rate of 20% since it was first

游客2024-01-13 60

问题 An investment has been growing at a fixed annual rate of 20% since it was first made; no portion of the investment has been withdrawn, and all interest has been reinvested. How much is the investment now worth?
(1) The value of the investment has increased by 44% since it was first made.
(2) If one year ago $600 had been withdrawn, today the investment would be worth 12% less than it is actually now worth.

选项 A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.

答案 B

解析 If the investment was initially worth $P, then after one year the investment was worth $1.2P, after two years the investment was worth 1.2($1.2P) = $1.44P, after three years the investment was worth 1.2($1.44P) = $1.728P, etc.
(1) Given that the investment was worth $(P + 0.44P) = $1.44P, it follows from the remarks above that the investment was first made two years ago. However, nothing is known about the value of P; NOT sufficient.
(2) Let $X be how much the investment was worth one year ago. Then the investment is now worth $1.2X. However, if $600 had been withdrawn from the investment one year ago, then the investment would have been worth $(X- 600) one year ago and the investment would have been worth $1.2(X- 600) = $(1.2X- 720) today. It is given that this amount, namely $(1.2X- 720), is 12 percent less than $1.2X. Therefore, 1.2X- 720 = (0.88)(1.2X).This equation can be solved for X, and using this value of X, the value of 1.2 X can be determined; SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.

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