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An investment of $1000 was made in a certain account and ear

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An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 12:28
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An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?

A. 16
B. 18
C. 20
D. 24
E. 30

[Reveal] Spoiler:
I have the solution presented by GMAT prep but it is not the way I like to do it. My strategy would simply be to find the interest rate. And then work backwards from the solutions to get the answer (an interest of 7000, or total of 8000).

But I'm having trouble calculating the rate here?

Can anyone help?

in 12 years he made 3000 in interest. So shouldn't it be 1000(r/100)^12 = 3000 ?? then solve for r ?

I keep getting a number in the 30s, or 36.... ugh.
[Reveal] Spoiler: OA
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 16:57
HI anon1,I think you miss the point " compound interest" , the formula must be

1000* (1+r)^12 = 4000 (1)
1000* (1+r)^x =8000 (2) ( x : is the number of years we must find)

(1): --> 1+r= (12 root of 4)
(2)--> (1+r)^x=( 12 root of 4)^x = 8
---> 4^(x/12) =8
2^(x/6)=2^3
x/6=3 >>>x=18

hope this help ^^
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 18:48
I'm sorry, I'm losing you.

I'm getting

(1) (1+r)^12 = 4
(2) (1+r)^x = 8

I don't know what goes on after this... not understanding your work

But why can't we just find out what the r first and then work backwards from the solutions to find the amount of years necessary to get an interest of 7000 / total of 8000
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 20:04
anon1 wrote:
I'm sorry, I'm losing you.

I'm getting

(1) (1+r)^12 = 4
(2) (1+r)^x = 8

I don't know what goes on after this... not understanding your work

But why can't we just find out what the r first and then work backwards from the solutions to find the amount of years necessary to get an interest of 7000 / total of 8000


(1): --> 1+r = √(12&4) (get 12 root of 4) then apply this to (2)
(2)--> (1+r)^x=√(12&4) ^x = 8
---> 4^(x/12) =8
2^(x/6)=2^3
x/6=3 >>>x=18

if you find r it hard for you to calculate !

Last edited by tiennguyen1701 on 24 Nov 2012, 20:17, edited 2 times in total.
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 20:09
Okay, I understand the math now....

Yikes, that is a lot of math to be able to do during the test....

dammit.
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 20:18
anon1 wrote:
Okay, I understand the math now....

Yikes, that is a lot of math to be able to do during the test....

dammit.

yup, i think both math and verbal are difficult :(
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 20:34
We just have to keep studying as hard as possible. Don't give up. We think we are studying hard?

they may studying twice as hard.
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 21:18
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anon1 wrote:
An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?

A. 16
B. 18
C. 20
D. 24
E. 30

I have the solution presented by GMAT prep but it is not the way I like to do it. My strategy would simply be to find the interest rate. And then work backwards from the solutions to get the answer (an interest of 7000, or total of 8000).

But I'm having trouble calculating the rate here?

Can anyone help?

in 12 years he made 3000 in interest. So shouldn't it be 1000(r/100)^12 = 3000 ?? then solve for r ?

I keep getting a number in the 30s, or 36.... ugh.


Its actually an easier question with a simpler approach.

Amount 1000 is invested for 12 yrs and yields 4000. Amount is compounded annually.
we need number of years it will take to yield 8000.

from 1000 to 4000 = 4 times
from 4000 to 8000 = 2 times.

if compounding is happening at same rate throughout, then
since, time required for 4 times = 12 yrs
=>time required for 2 times = 6 yrs

Total time from initial = 12+6 = 18 yrs
Ans B.
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 21:32
YES YES YES YES YES

THANK YOU SO MUCH.

I knew there was an elegant way to do this. I just could not figure it out... I have a personal theory that almost every GMAT problem can be solved with basic arithmetic and reasoning, and that was it VIPS. You are freaking awesome.
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 24 Nov 2012, 21:40
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anon1 wrote:
YES YES YES YES YES

THANK YOU SO MUCH.

I knew there was an elegant way to do this. I just could not figure it out... I have a personal theory that almost every GMAT problem can be solved with basic arithmetic and reasoning, and that was it VIPS. You are freaking awesome.

ha ha.. :-D
wish could have shown that on the test too :-(
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 25 Nov 2012, 16:50
Vips0000 wrote:
anon1 wrote:
An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?

A. 16
B. 18
C. 20
D. 24
E. 30

I have the solution presented by GMAT prep but it is not the way I like to do it. My strategy would simply be to find the interest rate. And then work backwards from the solutions to get the answer (an interest of 7000, or total of 8000).

But I'm having trouble calculating the rate here?

Can anyone help?

in 12 years he made 3000 in interest. So shouldn't it be 1000(r/100)^12 = 3000 ?? then solve for r ?

I keep getting a number in the 30s, or 36.... ugh.


Its actually an easier question with a simpler approach.

Amount 1000 is invested for 12 yrs and yields 4000. Amount is compounded annually.
we need number of years it will take to yield 8000.

from 1000 to 4000 = 4 times
from 4000 to 8000 = 2 times.

if compounding is happening at same rate throughout, then
since, time required for 4 times = 12 yrs
=>time required for 2 times = 6 yrs

Total time from initial = 12+6 = 18 yrs
Ans B.


Hey Vips,

I tried to figure out

from 1000 to 4000 = 4 times
from 4000 to 8000 = 2 times.

But couldn't :(

You mean 1000 to 4000 = 4*1000
4000 to 8000 = 2 *2000

If so how u took first as 1000 and next as 2000 ..... Or any other logic?

Can you brief it plzzz... !!!
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 26 Nov 2012, 00:36
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shanmugamgsn wrote:
Heyy Vips,

I tried to figure out

from 1000 to 4000 = 4 times
from 4000 to 8000 = 2 times.

But couldn't :(

You mean 1000 to 4000 = 4*1000
4000 to 8000 = 2 *2000

If so how u took first as 1000 and next as 2000 ..... Or any other logic?

Can you brief it plzzz... !!!


An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?

A. 16
B. 18
C. 20
D. 24
E. 30

In 12 years the investment quadrupled (from $1,000 to $4,000).

Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $4,000 to $8,000).

Therefore, 12+6=18 years are needed $1,000 to increase to $8,000.

Answer: B.

Hope it's clear.
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 22 Jan 2014, 20:07
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Re: An investment of $1000 was made in a certain account and ear [#permalink] New post 06 Jun 2014, 09:10
I used a logical approach to solve this:
In 12 years, the investment doubled twice. Therefore, in the first 6 years, the investment doubled from 1000 to 2000, and in the next 6 years the investment doubled again from 2000 to 4000. Since the rate of return remains the same, the investment will take another 6 years to double from 4000 to 8000.
Total time is 12+6=18
Re: An investment of $1000 was made in a certain account and ear   [#permalink] 06 Jun 2014, 09:10
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