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compound interest

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Manager
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compound interest [#permalink]  14 Feb 2011, 19:25
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Difficulty:

55% (hard)

Question Stats:

64% (02:44) correct 36% (01:37) wrong based on 53 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]  15 Feb 2011, 06:39
1
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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]  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]  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... _________________ SVP Joined: 16 Nov 2010 Posts: 1680 Location: United States (IN) Concentration: Strategy, Technology Followers: 31 Kudos [?]: 348 [0], given: 36 Re: compound interest [#permalink] 15 Feb 2011, 19:22 Please explain this bit : "I divided the principal", i.e, how does division of principal yield interest ? _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Manager Joined: 07 Jun 2010 Posts: 86 Followers: 1 Kudos [?]: 25 [0], given: 0 Re: compound interest [#permalink] 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 Math Forum Moderator Joined: 20 Dec 2010 Posts: 2031 Followers: 138 Kudos [?]: 1136 [1] , given: 376 Re: compound interest [#permalink] 15 Feb 2011, 23:07 1 This post received KUDOS 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. _________________ Director Status: Up again. Joined: 31 Oct 2010 Posts: 543 Concentration: Strategy, Sustainability GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 Followers: 17 Kudos [?]: 149 [0], given: 75 Re: compound interest [#permalink] 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? _________________ My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html Manager Joined: 17 Feb 2011 Posts: 201 Concentration: Real Estate, Finance Schools: MIT (Sloan) - Class of 2014 GMAT 1: 760 Q50 V44 Followers: 36 Kudos [?]: 559 [0], given: 70 Re: compound interest [#permalink] 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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