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Jon invested $20000 in a certain stock exactly three years ago. The va

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Jon invested $20000 in a certain stock exactly three years ago. The va [#permalink]

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New post 24 Dec 2017, 22:42
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Jon invested $20000 in a certain stock exactly three years ago. The value of the stocks increased by 15 percent during the first year, increased by 10 percent during the second year, and decreased by 5 percent during the third year. What is the value of the stocks today?

A. $22,000
B. $24,000
C. $24,035
D. $26,000
E. $26,565
[Reveal] Spoiler: OA

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Re: Jon invested $20000 in a certain stock exactly three years ago. The va [#permalink]

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New post 24 Dec 2017, 23:43
Bunuel wrote:
Jon invested $20000 in a certain stock exactly three years ago. The value of the stocks increased by 15 percent during the first year, increased by 10 percent during the second year, and decreased by 5 percent during the third year. What is the value of the stocks today?

A. $22,000
B. $24,000
C. $24,035
D. $26,000
E. $26,565


We'll show two ways to solve this problem.

The first is an extremely fast approximation which is an Alternative approach.
We gained 10% then 15% then lost 5% over the 3 years.
Had our interest been exactly 10 + 15 - 5 = 20% then the answer would be (B) - $24,000.
But - due to cumulative interest and the fact that losing 5% is more money than gaining 5%, we know our answer is near to $24,000 but not exactly $24,000.
Since (C) is the only such answer it must be correct and we can move on having done almost no (potentialy confusing) calculations.

The Precise approach is standard - calculate the total increase
20,000 * 1.1 = 22,000
22,000 *1.15 = 22,000 + 2,200 + 1,100 = 25,300
25,300 * 0.95 = 25,300 - 2530/2 = 25,300 - 1265 = 24,035
As above, (C) is our answer.
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Re: Jon invested $20000 in a certain stock exactly three years ago. The va [#permalink]

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New post 25 Dec 2017, 11:16
Bunuel wrote:
Jon invested $20000 in a certain stock exactly three years ago. The value of the stocks increased by 15 percent during the first year, increased by 10 percent during the second year, and decreased by 5 percent during the third year. What is the value of the stocks today?

A. $22,000
B. $24,000
C. $24,035
D. $26,000
E. $26,565


Value of Stock today is: \(20000*(1+0.15)*(1+0.10)*(1-0.05)=20000*1.15*1.1*0.95=24035\)

(C) is the answer.
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Re: Jon invested $20000 in a certain stock exactly three years ago. The va [#permalink]

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New post 25 Dec 2017, 11:25
Jon invested $20000 in a certain stock exactly three years ago. The value of the stocks-

Increased by 15 percent during the first year, therefore, at the end of year 1 the value of the stock was $20k * 1.15= $23k.
Further increased by 10 percent during the second year, therefore, at the end of year 2 the value of the stock was $23k * 1.10= $25.3k
Eventually decreased (unfortunately) by 5 percent during the third year, so, at the end of year 3 the value of stock is $25.3 *.95= $24,035. Hence C.
Re: Jon invested $20000 in a certain stock exactly three years ago. The va   [#permalink] 25 Dec 2017, 11:25
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