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Amy’s retirement portfolio contains only stocks and bonds. At the begi

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New post 22 Nov 2016, 05:52
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Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%

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Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 22 Nov 2016, 06:43
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Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%


B

Let the total value of her portfolio be $100,000
then the value of her stocks will be $60,000 and the value of her bonds will be $40,000
Her total portfolio value increased by 8% to $108,000
her stock holding value increased by 10% to $66,000
so her bond increased to $108,000-$66,000= $42000
required = $42,000-$40,000/$40,000 = 1/20 = 5%
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Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 22 Nov 2016, 08:14
Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%


As usual a tabular approach works best for me -
Attachment:
Capture.PNG
Capture.PNG [ 5.25 KiB | Viewed 1553 times ]


Thus total value of Bond at the end of 2016 is 420 ( ie, 1080 - 660 )

So, Per unit value of Bond at the end of 2016 is \(\frac{420}{40} = 10.50\)

Hence, percentage increase is \(\frac{0.50}{10}*100 =5\)%, answer will be (B)

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Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 22 Feb 2017, 22:08
Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%


Official solution from Veritas Prep.

If you recognize that this is a weighted average problem, you can employ the weighted average Mapping Strategy to solve. You know that the weighted average of growth is 8% and that the growth from stocks is 10%, so you can draw your map accordingly:

x------------8%------10%

You also know that the ratio of stocks to bonds is 3:2, meaning that the distances from x% to 8% and from 8% to 10% will follow a ratio of 3:2, with the more heavily-weighted stocks (10%) having the shorter distance. So since there are two places from 8 to 10 that means that x will be three places from 8, meaning that the answer is 5%, answer choice B.

Alternatively, you can solve algebraically or by picking numbers. Since you're working with percent changes, if you want to pick numbers a good place to start is to pick a number like $1,000 for her total value. That would mean that she started with $600 in stocks, from which a 10% increase would mean that stocks gained her $60. Since her total value increased from $1000 to $1080, that means that bonds needed to account for the other 20% gain. Given a starting value of $400 in bonds, you can then ask what percent of $400 is $20, and the answer is 5%.
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Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 16 Sep 2017, 11:35
Stupid question. :-) Trying to solve this with weighted average formula, but for some reason it doesn't work. (x is bond return)
\(\frac{0.6*10+0.4*x}{10+x}\)= 8

6+0.4x=80+8x

-7.6x= 74
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Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 16 Sep 2017, 12:45
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Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%

inter , I ran into exactly the same problem.

I don't use the scale method or alligation.

I stayed with weighted average, but I used different numbers and got the answer.

I kept everything in decimals because x is a percent; x is really \(\frac{x}{100}\).

This weighted average works, where x = percent return on bonds:

(.6)(.1) + (.4)(x) = .08

.06 + .4x = .08
.4x = .02

x = \(\frac{.02}{.4}\)

x = .05 = 5 percent

ANSWER B
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Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 16 Sep 2017, 13:09
Thanks - just realized everything is already in percents.
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Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 16 Sep 2017, 13:51
inter wrote:
Thanks - just realized everything is already in percents.

inter - this question is really basic, but now I'm a little scrambled :?: when you say "everything is already in percents," what, in weighted average terms, do you mean?

I usually work with rounder numbers (I change decimal percentages to integers). I went wrong by multiplying the weights, instead of the percentages, by 100 to get rounder numbers.

I also know that I could multiply the percentages by 100 and it works (result is .4x = 2, x = 5, and I've included the "percent" already by multiplying all the percents by 100).

For the future: if "everything is already in percents," do you find that it is easier to just leave them that way? Or did you intend something else?
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Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 14 Dec 2017, 08:21
Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%



We can let p = the value of Amy’s portfolio at the beginning of 2016.

We are given that she initially had 60% stocks or 0.6p and 40% bonds or 0.4p. Since the total value of her stock holdings increased by 10% and the total value of her portfolio increased by 8%, we can create the following equation in which n is the percentage increase of the bond holdings.

1.1(0.6p) + (1 + n/100)(0.4p) = 1.08p

0.66p + [(100 + n)/100)](0.4p) = 1.08p

0.66p + [(40p + 0.4pn)/100] = 1.08p

Multiplying the entire equation by 100, we have:

66p + 40p + 0.4pn = 108p

106p + 0.4pn = 108p

0.4pn = 2p

0.4n = 2

n = 2/0.4 = 5

Answer: B
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Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

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New post 12 Jan 2018, 14:10
Hi All,

This question can be solved in a number of different ways, including algebraically and by TESTing VALUES. It's ultimately a Weighted Average question though, so here's how you can approach it with that formula:

Since we have 60% stocks and 40% bonds, the ratio is 6/4 = 3/2... meaning that for every 3 stocks we have 2 bonds. We know that the value of the stocks increased by 10% and the TOTAL value of the portfolio increased by 8%. We're asked to find the increase in the value of the bonds....

X = increase in value of the bonds

[3(10) + 2(X)] / (5) = 8
30 + 2X = 40
2X = 10
X = 5

Thus, the value of the bonds increased by 5%

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Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi &nbs [#permalink] 12 Jan 2018, 14:10
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