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# A certain sum was invested in a high-interest bond for which

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A certain sum was invested in a high-interest bond for which [#permalink]  16 Mar 2011, 06:49
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Difficulty:

65% (hard)

Question Stats:

39% (02:03) correct 61% (01:00) wrong based on 21 sessions
A certain sum was invested in a high-interest bond for which the interest is compounded monthly. The bond was sold x number of months later, where x is an integer. If the value of the original investment doubled during this period, what was the approximate amount of the original investment in dollars?

(1) The interest rate during the period of investment was greater than 39 percent but less than 45 percent.
(2) If the period of investment had been one month longer, the final sale value of the bond would have been approximately $2,744. [Reveal] Spoiler: OA Math Forum Moderator Joined: 20 Dec 2010 Posts: 2035 Followers: 135 Kudos [?]: 1107 [1] , given: 376 Re: A certain sum was invested in a high-interest bond for which [#permalink] 16 Mar 2011, 07:40 1 This post received KUDOS punyadeep wrote: Q A certain sum was invested in a high-interest bond for which the interest is compounded monthly. The bond was sold x number of months later, where x is an integer. If the value of the original investment doubled during this period, what was the approximate amount of the original investment in dollars? (1) The interest rate during the period of investment was greater than 39 percent but less than 45 percent. (2) If the period of investment had been one month longer, the final sale value of the bond would have been approximately$2,744.

Investment = $P time: x months = x/12 years Periods = n = 12 Return after application of the compound Interest for x months; $$P(1+\frac{r}{n})^{nt}$$ $$P(1+\frac{r}{12})^{12*x/12}$$ $$P(1+\frac{r}{12})^x$$ It is given that the investment doubles after x months; $$P(1+\frac{r}{12})^x=2P$$ $$(1+\frac{r}{12})^x=2$$ r and x are unknown 1. 0.4<=r<=0.44 $$(1+\frac{0.4}{12})^x=(1.033)^x = 2$$ to $$(1+\frac{0.44}{12})^x=(1.036)^x=2$$ x can be found; but we don't know P. Not Sufficient. 2. $$P(1+\frac{r}{12})^{(x+1)}=2744$$ $$P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744$$ $$2P*(1+\frac{r}{12})=2744$$ We still have two unknowns. Not Sufficient. Combining both; r= 0.4 $$2P*(1+\frac{0.4}{12})=2744$$ Now, we can get approx value of P. Ans: "C" _________________ Intern Joined: 08 Mar 2011 Posts: 25 Followers: 0 Kudos [?]: 15 [0], given: 31 Re: A certain sum was invested in a high-interest bond for which [#permalink] 16 Mar 2011, 08:24 thnx so much fluke regards GMAT Instructor Joined: 24 Jun 2008 Posts: 978 Location: Toronto Followers: 281 Kudos [?]: 799 [0], given: 3 Re: A certain sum was invested in a high-interest bond for which [#permalink] 16 Mar 2011, 21:19 Where is this question from? It makes no sense, in DS, to ask for the 'approximate value' of something -- how could you possibly know what information would be sufficient? If I ask the following question: What is the approximate value of x? 1. 3 < x < 5 2. 4 < x < 4.5 Is Statement 1 sufficient? Statement 2? You can't possibly know. It's a nonsensical question to ask in DS, so I wouldn't use other questions from the same source. _________________ Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details. Private GMAT Tutor based in Toronto Current Student Joined: 17 Mar 2011 Posts: 453 Location: United States (DC) Concentration: General Management, Technology GMAT 1: 760 Q49 V45 GPA: 3.37 WE: Information Technology (Consulting) Followers: 11 Kudos [?]: 163 [0], given: 5 Re: A certain sum was invested in a high-interest bond for which [#permalink] 17 Mar 2011, 06:10 Good point Ian, based on (2) I could easily say "initial investment is between$0 and $1372, approximately" Senior Manager Joined: 08 Nov 2010 Posts: 422 WE 1: Business Development Followers: 7 Kudos [?]: 46 [0], given: 161 Re: A certain sum was invested in a high-interest bond for which [#permalink] 18 Mar 2011, 09:37 Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. _________________ Math Forum Moderator Joined: 20 Dec 2010 Posts: 2035 Followers: 135 Kudos [?]: 1107 [0], given: 376 Re: A certain sum was invested in a high-interest bond for which [#permalink] 18 Mar 2011, 10:00 144144 wrote: Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. From the stem, please see the [highlight]highlighted[/highlight] part. fluke wrote: Investment =$P
time: x months = x/12 years
Periods = n = 12

Return after application of the compound Interest for x months;

$$P(1+\frac{r}{n})^{nt}$$
$$P(1+\frac{r}{12})^{12*x/12}$$
$$P(1+\frac{r}{12})^x$$
It is given that the investment doubles after x months;
$$P(1+\frac{r}{12})^x=2P$$ [highlight]--------------A[/highlight]
$$(1+\frac{r}{12})^x=2$$

r and x are unknown

1. 0.4<=r<=0.44
$$(1+\frac{0.4}{12})^x=(1.033)^x = 2$$
to
$$(1+\frac{0.44}{12})^x=(1.036)^x=2$$

x can be found; but we don't know P.
Not Sufficient.

2.
$$P(1+\frac{r}{12})^{(x+1)}=2744$$
$$P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744$$
[highlight]Substitute from equation A[/highlight]
$$2P*(1+\frac{r}{12})=2744$$
We still have two unknowns.
Not Sufficient.

Combining both;

r= 0.4
$$2P*(1+\frac{0.4}{12})=2744$$

Now, we can get approx value of P.

Ans: "C"

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Re: A certain sum was invested in a high-interest bond for which [#permalink]  18 Mar 2011, 19:05
Expert's post
This question reminds me:

Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest.

i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years.
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Re: A certain sum was invested in a high-interest bond for which [#permalink]  19 Mar 2011, 10:54
Not a Gmat question. Do not waste your time.
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A certain sum was invested in a high-interest bond for which the inter [#permalink]  15 Nov 2011, 14:44
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A certain sum was invested in a high-interest bond for which the interest is compounded monthly. The bond was sold x number of months later, where x is an integer. If the value of the original investment doubled during this period, what was the approximate amount of the original investment in dollars?

(1) The interest rate during the period of investment was greater than 39 percent but less than 45 percent.
(2) If the period of investment had been one month longer, the final sale value of the bond would have been approximately $2,744. can someone please have a look into this and let me know how to solve this? _________________ Best Regards, E. MGMAT 1 --> 530 MGMAT 2--> 640 MGMAT 3 ---> 610 GMAT ==> 730 Current Student Joined: 16 Sep 2010 Posts: 227 Location: United States Concentration: Finance, Real Estate GMAT 1: 740 Q48 V42 Followers: 7 Kudos [?]: 72 [0], given: 2 Re: A certain sum was invested in a high-interest bond for which the inter [#permalink] 15 Nov 2011, 15:47 So we now there was an investment in a bond that compounds monthly for X months. X is a whole number so no fractional months, and that the value of the bond doubled in our X months of investment. Statement 1 - gives us not info about value - granted we can back into a range of X but a dollar amount is impossible - insuff. Statement 2- gives us a value at X+1, but its impossible to determine the starting value as we do not know either the interest rate or the starting value - insuff. Together you have a range of rates and a X-1 ending value. Since the starting value doesn't have to be an integer and the interest rate doesn't have to be an integer either their are a number of possible answers for this. I would say it should be E. Manager Joined: 12 Jul 2011 Posts: 154 Concentration: Operations, Strategy GMAT 1: 680 Q46 V37 WE: Engineering (Telecommunications) Followers: 0 Kudos [?]: 20 [1] , given: 42 Re: A certain sum was invested in a high-interest bond for which the inter [#permalink] 15 Nov 2011, 20:54 1 This post received KUDOS Answer is C. You can find a good explanation here: http://www.urch.com/forums/gmat-math/20537-interest-rates.html Manager Joined: 08 Sep 2011 Posts: 77 Concentration: Finance, Strategy Followers: 3 Kudos [?]: 2 [0], given: 5 Re: A certain sum was invested in a high-interest bond for which the inter [#permalink] 16 Nov 2011, 09:05 I decided on C after three mins, but it was more of a guess off of what I know rather than confirmation. Just hope you don't get one of these on the test Manager Joined: 15 Mar 2012 Posts: 71 Followers: 0 Kudos [?]: 3 [0], given: 20 Re: A certain sum was invested in a high-interest bond for which [#permalink] 10 Sep 2013, 17:19 VeritasPrepKarishma wrote: This question reminds me: Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest. i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years. Couldn't the following give multiple values of x (may be with a minor difference each)? So, we wouldn't have a single answer to the question & hence 1 & 2 aren't sufficient together. SO, the answer shd be E. Please correct me if I'm wrong. Thank you. ********************************** (1+\frac{0.4}{12})^x=(1.033)^x = 2 to (1+\frac{0.44}{12})^x=(1.036)^x=2 x can be found; but we don't know P. ********************************** Math Expert Joined: 02 Sep 2009 Posts: 27215 Followers: 4227 Kudos [?]: 41002 [0], given: 5654 Re: A certain sum was invested in a high-interest bond for which [#permalink] 11 Sep 2013, 02:42 Expert's post divineacclivity wrote: VeritasPrepKarishma wrote: This question reminds me: Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest. i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years. Couldn't the following give multiple values of x (may be with a minor difference each)? So, we wouldn't have a single answer to the question & hence 1 & 2 aren't sufficient together. SO, the answer shd be E. Please correct me if I'm wrong. Thank you. ********************************** (1+\frac{0.4}{12})^x=(1.033)^x = 2 to (1+\frac{0.44}{12})^x=(1.036)^x=2 x can be found; but we don't know P. ********************************** This is a poor quality question. Check here: a-certain-sum-was-invested-in-a-high-interest-bond-for-which-110991.html#p893606 _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 4767 Followers: 296 Kudos [?]: 52 [0], given: 0 Re: A certain sum was invested in a high-interest bond for which the inter [#permalink] 19 Nov 2014, 10:32 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: A certain sum was invested in a high-interest bond for which the inter [#permalink] 19 Nov 2014, 10:32 Similar topics Replies Last post Similar Topics: A certain sum was invested in a high-interest bond for which the inter 0 19 Nov 2014, 10:32 2 Samantha invests i1 dollars in bond X, which pays r1 19 02 Oct 2010, 10:56 If$4500 dollars was invested in a bond fund when the price 5 23 Jul 2007, 17:40
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