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compound interest

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compound interest [#permalink] New post 14 Feb 2011, 19:25
00:00
A
B
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E

Difficulty:

  55% (hard)

Question Stats:

62% (02:38) correct 38% (01:41) wrong based on 47 sessions
An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
A. 4
B. 5
C. 6
D. 7
E. 8
[Reveal] Spoiler: OA

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Re: compound interest [#permalink] New post 15 Feb 2011, 06:39
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By the Compound Interest formula :

A = P(1 + r/100)^nt

It comes to (1.341)^n = 3 (since A = 3P, and t = 1)

On multiplying 1.341 further with itself, it can be seen that n = 4, so answer is A.
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Re: compound interest [#permalink] New post 15 Feb 2011, 07:24
Please correct me if I am wrong but it seems you need to workout the multiplication of 1.341 at least 3 times very quickly which seems rather daunting given the tight time constraints of the GMAT..

Is there a faster way of doing this?
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Re: compound interest [#permalink] New post 15 Feb 2011, 09:29
drifting wrote:
Please correct me if I am wrong but it seems you need to workout the multiplication of 1.341 at least 3 times very quickly which seems rather daunting given the tight time constraints of the GMAT..

Is there a faster way of doing this?


I agree; I divided the principal by 3 by considering approx 33.33% and rounded the value to greater nearest integer;

1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100)

;4 years;

Perhaps there is a better way...
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Re: compound interest [#permalink] New post 15 Feb 2011, 19:22
Please explain this bit :

"I divided the principal", i.e, how does division of principal yield interest ?
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Re: compound interest [#permalink] New post 15 Feb 2011, 19:58
I rounded to 33.3333% or 1/3

Since the formula is:

P1 = P0 (1 + r)^n

3 = 1(1+.333333333)^n

3 = 1(4/3)^n

3= (4^n / 3^n)

From here, start with n = 4 and see if the ratio is greater or less than 3

4^4 = 16^2 = 256
3^4 = 9^2 = 81

81*3 = 243...256>243 so 4 is sufficient if the rate were 33.333%. Since the rate is larger than 33.33% it is definitely sufficient
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Re: compound interest [#permalink] New post 15 Feb 2011, 23:07
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subhashghosh wrote:
Please explain this bit :

"I divided the principal", i.e, how does division of principal yield interest ?


We can quickly get the percentage if we divide the number for which the percentage is found:
such as,
20% of 40 = 40/5 = 8
10% of 80 = 80/10 = 8
50% of 35 = 35/2 = 17.5
33.33% of 100 = 100/3 = 33 approx

Since 34.1% is close to 33.33%; we can divide the number(or principal by 3 and get the interest); Investment: $100

1st year: 34.1% interest is gotten back on 100: 100/3 = 33.33 approx $34: New principal becomes: Principal+Interest: 100+34=134

2nd year: 34.1% interest on 134; 134/3 = 45: Total: 134+45 = 179(new principal)
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100); end of 4 years, the return was already more than triple.
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Re: compound interest [#permalink] New post 17 Feb 2011, 04:38
subhashghosh wrote:
By the Compound Interest formula :

A = P(1 + r/100)^nt

It comes to (1.341)^n = 3 (since A = 3P, and t = 1)

On multiplying 1.341 further with itself, it can be seen that n = 4, so answer is A.


Thanks for the explanation!

But what if this equation consists of a number larger than 3, say 300!

Another question, Is the T in your formula really necessary?
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Re: compound interest [#permalink] New post 17 Feb 2011, 08:55
I liked this approach. This question is not difficult, but with this approach it can be done more quickly as well.

fluke wrote:
drifting wrote:
Please correct me if I am wrong but it seems you need to workout the multiplication of 1.341 at least 3 times very quickly which seems rather daunting given the tight time constraints of the GMAT..

Is there a faster way of doing this?


I agree; I divided the principal by 3 by considering approx 33.33% and rounded the value to greater nearest integer;

1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100)

;4 years;

Perhaps there is a better way...
Re: compound interest   [#permalink] 17 Feb 2011, 08:55
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