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# On a certain date, Pat invested $10,000 at x percent annual  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Current Student Joined: 11 May 2008 Posts: 560 Followers: 7 Kudos [?]: 64 [0], given: 0 On a certain date, Pat invested$10,000 at x percent annual [#permalink]  22 Jul 2008, 17:59
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On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be$40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24 [Reveal] Spoiler: OA Last edited by Bunuel on 02 Jul 2014, 09:15, edited 1 time in total. Renamed the topic, edited the question, added the OA and moved to PS forum. Manager Joined: 05 Jul 2008 Posts: 139 GMAT 1: Q V GMAT 2: 740 Q51 V38 Followers: 2 Kudos [?]: 83 [3] , given: 40 Re: On a certain date, Pat invested$10,000 at x percent annual [#permalink]  22 Jul 2008, 20:13
3
KUDOS
arjtryarjtry wrote:
On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be$40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24 x- interest rate 80.000= 10.000 (1+x)^year => 8=(1+x)^year 40.000=10.000 . (1+x)^12 => 4= (1+x)^12 =>2= (1+x)^6 => 8 = (1+x)^ 18 So, after 18 years, the total value of the investment plus interest will increase to$80,000.
Current Student
Joined: 11 May 2008
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 02 Sep 2008, 18:50 1 This post was BOOKMARKED On a certain date, Pat invested$10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to$80,000?
A. 15
B. 16
C. 18
D. 20
E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps...
also mention, for variations in the problems, how does one approach???
SVP
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 02 Sep 2008, 22:24 arjtryarjtry wrote: On a certain date, Pat invested$10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to$80,000?
A. 15
B. 16
C. 18
D. 20
E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps...
also mention, for variations in the problems, how does one approach???

your second post blocked my post.

i cannot do it without calculator or computer and also beleieve this is not real gmat type question cuz its very difficult to get the value without those machines.

if i were to choose during the test, would go for 18/ or 20. probably 18 cuz not it wont take too long to get the value doubled....
_________________
Current Student
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 03 Sep 2008, 00:22 given 40000=10000(1+x/100)^12 or 4 ^1/12 = (1+x/100) or x/100 = 4^1/12-1........A asked 80000=10000(1+x/100)^n..............b n=? substitute value of x/100 from A in B. 8 = (1+4^1/12-1)^n or 8= 4^n/12 2^3=2^2n/12 n=18 ans = C SVP Joined: 07 Nov 2007 Posts: 1824 Location: New York Followers: 29 Kudos [?]: 573 [1] , given: 5 Re: On a certain date, Pat invested$10,000 at x percent annual [#permalink]  03 Sep 2008, 05:31
1
KUDOS
arjtryarjtry wrote:
On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be$40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24 for compound interest problems, when the time is large, then how does one approach??? dont just give the steps... also mention, for variations in the problems, how does one approach??? 40k = 10k(1+x/100)^12 --> 4=(1+x/100)^12 --> (1+x/100)^6=2 80k=40k(1+x/100)^n --> (1+x/100)^n =2 =(1+x/100)^6 n=6 Total years = 12+6=18 _________________ Your attitude determines your altitude Smiling wins more friends than frowning Intern Joined: 03 Sep 2008 Posts: 22 Followers: 0 Kudos [?]: 7 [6] , given: 0 Re: On a certain date, Pat invested$10,000 at x percent annual [#permalink]  03 Sep 2008, 11:17
6
KUDOS
$40,000 is 4 times the original amount. Therefore it doubled twice in 12 years. Therefore its doubling time is 6.$80,000 is double $40,000 so another 6 years will get us to$80,000.

Therefore 12+6=18 is the necessary amount of time.
Senior Manager
Joined: 04 Jan 2006
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 03 Sep 2008, 11:47 arjtryarjtry wrote: On a certain date, Pat invested$10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to$80,000?
A. 15
B. 16
C. 18
D. 20
E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps...
also mention, for variations in the problems, how does one approach???

Let's simplify this question.

First equation; 40,000 = 10,000(1 + x)^12
Given that (1 + x) = a and rearrange the equation above we get
4 = a^12 = 2^2
So now we know that a^12 = (a^6)^2 = 2^2
Therefore, (a^6) = 2

Second equation; 80,000 = 10,000(1 + x)^n
Or 8 = a^n
2^3 = a^n
(a^6)^3 = a^n = a^18 ---- (since a^6 = 2)

therefore, n = 18. C is the answer
Manager
Joined: 09 Jul 2007
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 03 Sep 2008, 12:42 Even though it looks like a tough question, it is actually not. 4 times in 12 yesrs = > 2 times in 6 years ( from 40K to 80K ). So total year = 12 +6 =18 Manager Joined: 20 May 2008 Posts: 57 Followers: 2 Kudos [?]: 6 [0], given: 1 Re: On a certain date, Pat invested$10,000 at x percent annual [#permalink]  02 Feb 2009, 01:35
$40,000 is 4 times the original amount. Therefore it doubled twice in 12 years. Therefore its doubling time is 6.$80,000 is double $40,000 so another 6 years will get us to$80,000.

Therefore 12+6=18 is the necessary amount of time.

________________________

is this the right method???
SVP
Joined: 29 Aug 2007
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 02 Feb 2009, 07:51 1 This post received KUDOS GMAT TIGER wrote: arjtryarjtry wrote: On a certain date, Pat invested$10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to$80,000?
A. 15
B. 16
C. 18
D. 20
E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps...
also mention, for variations in the problems, how does one approach???

your second post blocked my post.

i cannot do it without calculator or computer and also beleieve this is not real gmat type question cuz its very difficult to get the value without those machines.

if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....

I found a method: Rule of 72.

Given an x% return, it takes 10,000 to quadralope 12 years.

So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00.
Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.

72/x+ 72/x = 12
x = 12% (though rate here is not very much required).

Again, 40,000.00 takes the same (72/x) no of years to double 80,000.00.

72/x = 6 years.

So altogather:
10,000 - 20,000 = 6 years
20,000 - 40,000 = 6 years
40,000 - 80,000 = 6 years
total 18 years.
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 02 Jul 2014, 05:45 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. _________________ Intern Joined: 13 May 2014 Posts: 29 GMAT Date: 11-01-2014 Followers: 0 Kudos [?]: 5 [0], given: 39 Re: On a certain date, Pat invested$10,000 at x percent annual [#permalink]  26 Jun 2015, 22:29
The key is to identify how quickly the money gets doubled..

for the current problem money gets doubled in every 6 years..

t=0 Investment = 10000
t=6 Investment= 20000
t=12 Investment = 40000..

Therefore for money to double from 40,000 to 80,000 it will take another 6 years. i.e 18years
Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 26 Jun 2015, 22:29 Similar topics Replies Last post Similar Topics: 8 Jill invests$10000 in an account that pays an annual rate 7 24 Jan 2013, 17:09
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