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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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33% (02:42) correct 66% (01:02) wrong based on 12 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. Math Forum Moderator Joined: 20 Dec 2010 Posts: 2058 Followers: 122 Kudos [?]: 815 [1] , given: 376 Re: compound intrest [#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" _________________ ~fluke Intern Joined: 08 Mar 2011 Posts: 24 Followers: 0 Kudos [?]: 5 [0], given: 31 Re: compound intrest [#permalink] 16 Mar 2011, 08:24 thnx so much fluke regards GMAT Instructor Joined: 24 Jun 2008 Posts: 967 Location: Toronto Followers: 232 Kudos [?]: 561 [0], given: 3 Re: compound intrest [#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: 10 Kudos [?]: 141 [0], given: 5 Re: compound intrest [#permalink] 17 Mar 2011, 06:10 Good point Ian, based on (2) I could easily say "initial investment is between$0 and $1372, approximately" Senior Manager Joined: 08 Nov 2010 Posts: 424 WE 1: Business Development Followers: 6 Kudos [?]: 28 [0], given: 161 Re: compound intrest [#permalink] 18 Mar 2011, 09:37 Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. Math Forum Moderator Joined: 20 Dec 2010 Posts: 2058 Followers: 122 Kudos [?]: 815 [0], given: 376 Re: compound intrest [#permalink] 18 Mar 2011, 10:00 144144 wrote: Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. From the stem, please see the [highlight]highlighted[/highlight] part. fluke wrote: Investment =$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: compound intrest [#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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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews CEO Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2792 Location: Malaysia Concentration: Technology, Entrepreneurship GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Followers: 155 Kudos [?]: 817 [0], given: 232 Re: compound intrest [#permalink] 19 Mar 2011, 10:54 Not a Gmat question. Do not waste your time. _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook Gmat test review : 670-to-710-a-long-journey-without-destination-still-happy-141642.html Intern Joined: 15 Mar 2012 Posts: 42 Followers: 0 Kudos [?]: 0 [0], given: 15 Re: compound intrest [#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: 16878 Followers: 2776 Kudos [?]: 17637 [0], given: 2233 Re: compound intrest [#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 _________________ Re: compound intrest [#permalink] 11 Sep 2013, 02:42 Similar topics Replies Last post Similar Topics: A certain sum was invested in a high-interest bond for which 5 25 Mar 2005, 01:28 A sum of money invested for a certain number of years at 8% 2 11 May 2005, 12:32 Instead of buying stocks and bonds, which are the 4 14 Mar 2007, 20:15 If$4500 dollars was invested in a bond fund when the price 5 23 Jul 2007, 17:40
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