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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?

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

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22 Nov 2016, 05:43

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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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22 Nov 2016, 07:14

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 [ 5.25 KiB | Viewed 1026 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) _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

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

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22 Feb 2017, 21:08

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?

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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16 Sep 2017, 10:35

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

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16 Sep 2017, 11:45

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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?

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

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16 Sep 2017, 12:51

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?

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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