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22 Jul 2008, 18:59
2
KUDOS
11
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Difficulty:

55% (hard)

Question Stats:

63% (02:56) correct 37% (02:18) wrong based on 189 sessions

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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, 10:15, 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: 3 Kudos [?]: 108 [5] , given: 40 Re: On a certain date, Pat invested$10,000 at x percent annual [#permalink]

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22 Jul 2008, 21:13
5
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2
This post was
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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.
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] ### Show Tags 02 Sep 2008, 19:50 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???
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Joined: 29 Aug 2007
Posts: 2491
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Kudos [?]: 762 [0], given: 19

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] ### Show Tags 02 Sep 2008, 23:24 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....
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

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### Show Tags

03 Sep 2008, 06:31
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 [?]: 10 [8] , given: 0 Re: On a certain date, Pat invested$10,000 at x percent annual [#permalink]

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03 Sep 2008, 12:17
8
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.
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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] ### Show Tags 03 Sep 2008, 12:47 2 This post was BOOKMARKED 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
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02 Feb 2009, 02:35
1
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.

________________________

is this the right method???
SVP
Joined: 29 Aug 2007
Posts: 2491
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Kudos [?]: 762 [2] , given: 19

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] ### Show Tags 02 Feb 2009, 08:51 2 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.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

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26 Jun 2015, 23:29
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
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Posts: 2383
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (D)
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01 Dec 2016, 20:46
Tricky little bugger...

Compound Interest Formula: P[1+(r/n)]^(nt)

10,000(1+x)^12 = 40,000
(1+x)^12 = 4
(1+x) = 4^(1/12)

10,000(1+x)^t = 80,000
(4^(1/12))^t = 8
(2^2)^(1/12) = 2^3
(2^(1/6)^t = 2^3

Bases are equal, so we can set the exponents equal to each other --> (1/6)t = 3 --> t = 18

C.
Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink] 01 Dec 2016, 20:46 Similar topics Replies Last post Similar Topics: Pat invested x dollars in a fund that paid 8 percent annual interest, 1 20 Jan 2017, 07:08 1 John invests$10,000 at the monthly constant compounded rate of annual 1 04 Jan 2017, 07:11
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