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Lucy invested $10,000 in a new mutual fund account exactly

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Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Answer: B.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.9 = 10,395

Answer B is correct.

The first equation is easy. In the second, first calculate 10% (1,100) and divide that by 2 (550). Add that to 11,000.
In the final equation, calculate 10% again (1,155) and subtract it from 11,550.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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Bunuel wrote:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705



This is a question of successive % change. This question ultimately reduces to a multiplication problem.
Final value after successive % change on $10,000 = $10,000 X 1.1 X 1.05 X .9
1.1 X 1.05 X .9 = 1.0395
Answer is B)
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 03 Sep 2012, 06:45
I also followed the same approach and got the answer as B.
But I am wondering if there is any better method of calculating in any problem with successive year interest rates given.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Answer: B.

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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 07 Sep 2012, 20:56
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10000 + 1000 = 11000
11000 + 550 = 11550
11550 * 0.9 = 10395
(B)
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 19 Oct 2012, 01:06
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Stupid lucy! If she sees that there is a crisis in the world and her accounts diminishes every year, why hasn't she redraw her money after the second year?!?... I multiplied the last year with 1.1 instead of 0.9 and i got the D answear... This is lucy's fault! :D
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 15 Dec 2012, 11:14
Bunuel wrote:
SOLUTION

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Answer: B.

Thank you for the answer Bunuel, but i was just wondering. When you chose the denominators for the different fractions, was your goal to get 10 000 in the denominator so we could cancel Lucy's initial investment? Smart move by the way ;)
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10395. So the answer is (B).
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 02 May 2013, 10:12
.10x10,000= $1,000 end of y1 = 11,000
.05x11,000= $550.00 end of y2 = 11,550
.10x11,550= 1,150 -1,155
(subtract y2 with the loss of y3) end of y3= 10,395
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 06 Aug 2014, 10:49
We can use successive percentage formula : a+b + ab/100

so in the first two years it will increase 10 + 5 + 10*5/100 = 15.5

and in the second and third year it will be : 15.5 - 10 - 15.5*10/100 = 3.95

so finally the investment will increase by 3.95 %
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 06 Aug 2014, 21:37
Percent increase over time: 1.1 * 1.05 * 0.9 = 1.0395

1.0395 * 10,000 $ = 10,395 $

B
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 10 Sep 2014, 02:43
Bunuel wrote:
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705

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Question: 31
Page: 156
Difficulty: 600


10,000*1.1--> 10% increase in the first year.
11000*1.05 --> 5% increase in second year
10% decrease from 11550 --> 10395
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 16 Nov 2014, 07:51
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I cut corners this way:
10% of 10 000=1000 (move the dot one spot)
next year you have 11 000
5% of 11 000= 550 (move the dot one spot 1100 = 10%, divide by two to get 5% 1100/2=550)
So then you have 11 550, and subtract 10% from this --> 11 550 - 1155. Well it has to be less than 11 000 since more than 1000 is subtracted (eliminating D & E), and it has to end in 5 since you're subtracting a number ending in five (eliminating A & C) that leaves only B.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 20 Nov 2014, 00:50
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Say initial value = 100 (avoiding 2 extra 00)

1st Yr >> 10% increase = 100 + 10 = 110

2nd Yr >> 5% increase = 110 + 5.5 = 115.5

3rd Yr >> 10% decrease = 115.5 - 11.55 = 103.95

Resultant = 103.95 * 100 = 10395

Answer = B
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 19 Dec 2015, 08:19
year 1 Increases 10% 1000 Value became 11000
Year 2 increase 5% 550 value became 11550
Year 3 decrease 10% 1155 value became 11550-1155 = $10395.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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Bunuel wrote:
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705


To determine the value of the account today we want to set up an expression showing the various percent increases and decreases.

Remember we are multiplying each percent increase or decrease against the original value of $10,000.

Also, we must remember that a 10% increase is the same as multiplying by 1.1, a 5% increase is the same as multiplying by 1.05, and a 10% decrease is the same as multiplying by 0.9. That is:

10,000(1.1)(1.05)(0.9)

Because the multiplication may get a bit complicated in the equation above, we should convert each decimal to a fraction, allowing us to reduce before multiplying.
Thus, we have:

10,000(11/10)(105/100)(9/10)

This is equivalent to: 10,000(11 x 105 x 9/10,000)

Thus we see the the two values of 10,000 cancel out, and we are left with:

11 x 105 x 9 = 99 x 105 = 10,395

Note: If you did not want to perform the multiplication of the final step, you could have used a combination of units digits and estimation to come to the correct answer. Keep in mind that the product of 99 and 105 will have a units digit of 5. That leaves us with only B ($10,395) and E ($12,705) as possible answer choices. Next, by rounding up 99 to 100 and multiplying 100 by 105 we get a product of 10,500. Because we rounded up and answer choice E is LARGER than 10,500, it’s not a possible answer choice. Thus, the correct answer is B, $10,395.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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Bunuel wrote:
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705



Start: $10,000

First year +10%
10% of $10,000 = $1000
So, we get $10,000 + $1000 = $11,000

Second year +5%
5% of $11,000 = $550
So, we get $11,000 + $550 = $11,550

Third year -10%
10% of $11,550 = $1,155
So, we get $11,550 - $1155 = $10,395

Answer: B

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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New post 08 Feb 2018, 11:13
Hi All,

Many GMAT Quant questions require 3-5 'steps' to get to the solution, so you shouldn't try to do all of the steps at once. Thankfully, the steps tend to be pretty easy to do, so you shouldn't rush through any of them and you should be sure to write everything on your pad (so that you can physically see the work).

Here, we're starting with $10,000. In the first year, the value increased by 10%....

Let's deal with THAT step right now:

10% of $10,000 = $1,000
New Total = $10,000 + $1,000 = $11,000

...increased by 5% during the second year....

Now we have $11,000, so the numbers will be a little different:

10% of $11,000 = $1,100
5% of $11,000 = $550
New Total = $11,000 + $550 = $11,550

...DECREASED by 10% during the third year...

10% of $11,550 = $1,155
New Total = $11,550 - $1,155 = $10,395

There's actually a great shortcut in this last calculation. If you look at the 'units digits' of the two numbers, you can deduce that when you subtract one from the other, you end up with a number that ends in 5... Take a good look at the answer choices; how many are LESS than $11,550 AND end in a 5?

Final Answer:
[Reveal] Spoiler:
B


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Re: Lucy invested $10,000 in a new mutual fund account exactly   [#permalink] 08 Feb 2018, 11:13
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