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# A sum of money doubles itself at a compound interest in 15 years. In

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
A sum of money doubles itself at a compound interest in 15 years. In  [#permalink]

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Updated on: 26 Feb 2019, 04:35
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Difficulty:

15% (low)

Question Stats:

75% (00:55) correct 25% (01:12) wrong based on 305 sessions

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A sum of money doubles itself at a compound interest in 15 years. In how may years it will become 8 times ??

A. 30 years

B. 40 years

C. 45 years

D. 50 years

E. 60 years

_________________

Originally posted by Bunuel on 07 Feb 2014, 03:56.
Last edited by Bunuel on 26 Feb 2019, 04:35, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A sum of money doubles itself at a compound interest in 15 years. In  [#permalink]

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13 Aug 2014, 02:15
5
1
Say initial amount = 100

Final amount = 800

100 >>>>>>>> 200 >>>>>>>>> 400 >>>>>>>>>> 800

........... 15 ............ 15 ................. 15

Total = 15*3 = 45

##### General Discussion
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Re: A sum of money doubles itself at a compound interest in 15 years. In  [#permalink]

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11 Aug 2014, 01:44
3
Let's say amount of money = $2, then 8 times = 16$

Then
Year 00 = 2 $Year 15 = 4$
Year 30 = 8 $Year 45 = 16$ --> this is our answer, hence C.
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Re: A sum of money doubles itself at a compound interest in 15 years. In  [#permalink]

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21 Jun 2017, 05:18
Bunuel wrote:
aimlockfire1 wrote:
A sum of money doubles itself at a compound interest in 15 years . In how may years it will become 8 times ??

a) 30 years

b) 40 years

c) 45 years

d) 50 years

e) 60 years

If the sum doubles (x2) in 15 years, then it to become 2*2*2 = 8 times as large it should double three times, so three 15 years time period are needed, which is 3*15 = 45 years.

If the lump sum is 8x then this represents a 2x^3 increase to

x(1 +r)^15(3)= 8x

Thus
"C"
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: A sum of money doubles itself at a compound interest in 15 years. In  [#permalink]

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26 Feb 2019, 04:36
Bunuel wrote:
A sum of money doubles itself at a compound interest in 15 years. In how may years it will become 8 times ??

A. 30 years

B. 40 years

C. 45 years

D. 50 years

E. 60 years

If the sum doubles (*2) in 15 years, then it to become 2*2*2 = 8 times as large it should double three times, so three 15 years time period are needed, which is 3*15 = 45 years.

_________________
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Joined: 08 Apr 2019
Posts: 9
Re: A sum of money doubles itself at a compound interest in 15 years. In  [#permalink]

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25 Apr 2019, 03:58
We can use the standard Compound interest formula for this -

let x be the amount of money invested

2x = x(1+ r/100)^15........................eq 1

Now to want to find the how much time it will take for 8x

Which is (eq1)^3

Hence 8x = x(1 +r/100)^45

Hence C
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Re: A sum of money doubles itself at a compound interest in 15 years. In  [#permalink]

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22 Aug 2019, 09:54
Bunuel wrote:
A sum of money doubles itself at a compound interest in 15 years. In how may years it will become 8 times ??

A. 30 years
B. 40 years
C. 45 years
D. 50 years
E. 60 years

$$a(1+r)^{(15)}=2a…(1+r)^{(15)}=2…(1+r)=2^{(1/15)}$$
$$(1+r)^x=8…(2^{(1/15)})^{x}=8…2^x=8^{(15)}…2^x=(2^3)^{(15)}…x=3•15=45$$

Re: A sum of money doubles itself at a compound interest in 15 years. In   [#permalink] 22 Aug 2019, 09:54
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