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# The number of years it would take for the value of an investment to do

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Math Expert
Joined: 02 Sep 2009
Posts: 47983
The number of years it would take for the value of an investment to do  [#permalink]

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31 Jul 2018, 00:28
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Question Stats:

56% (01:24) correct 44% (01:18) wrong based on 36 sessions

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The number of years it would take for the value of an investment to double, at 26% interest compounded annually, is approximately which of the following?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

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Re: The number of years it would take for the value of an investment to do  [#permalink]

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31 Jul 2018, 01:53
Bunuel wrote:
The number of years it would take for the value of an investment to double, at 26% interest compounded annually, is approximately which of the following?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

As we're explicitly asked to estimate, we won't bother with exact calculations.
This is an Alternative approach.

If we start with 100 and increase every year by 25% (which is exactly 1/4 so easier to calculate than 26%)
after 1 year we'd have 100 + 100/4 = 125,
after 2 years we'd have 125 + 125/4 = about 125 + 30 = 155
after 3 years we'd have about 155 + 155/4 = about 155 + 40 = 195.
This is very nearly double what we started!

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Save up to $250 on examPAL packages (special for GMAT Club members) Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3786 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: The number of years it would take for the value of an investment to do [#permalink] ### Show Tags 31 Jul 2018, 07:46 1 Bunuel wrote: The number of years it would take for the value of an investment to double, at 26% interest compounded annually, is approximately which of the following? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 $$A = P(1 + \frac{r}{100})^n$$ Or, $$2p = p(1 + \frac{26}{100})^n$$ Or, $$2 = (1 + \frac{26}{100})^n$$ Or, $$2 = (1 + \frac{26}{100})^n$$ Or, $$2 = (\frac{126}{100})^n$$ Or, $$2 = 1.26^n$$ Now calculate , $$1.26^2 = 1.5876$$ And $$1.26^3 = 2.00$$, Thus Answer must be (B) 3 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) SC Moderator Joined: 22 May 2016 Posts: 1907 The number of years it would take for the value of an investment to do [#permalink] ### Show Tags 01 Aug 2018, 18:38 Bunuel wrote: The number of years it would take for the value of an investment to double, at 26% interest compounded annually, is approximately which of the following? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Agreed, estimation is the way to go. A compound interest rate of 26% translates into a multiplier of 1.26. Change to 1.25 $$1.25=1\frac{25}{100}=1\frac{1}{4}=\frac{5}{4}$$ Imagine 1 in an account. Multiply $$1*\frac{5}{4}*\frac{5}{4}*\frac{5}{4}$$ ... until the numerator is about twice the denominator. Each time the multiplier gets used = 1 year has elapsed (the multiplier is being used at the end of each year, with a first year base of 1) $$1*\frac{5}{4}*\frac{5}{4}*\frac{5}{4}=\frac{125}{64}$$ => 125 is $$\approx$$ double 64 Number of years? $$\frac{5}{4}$$ was used three times, i.e., at the end of each of 3 years Answer B Same as above with$1 and years shown

Begin: $$1=>$$End Year 1: $$(1*\frac{5}{4})=\frac{5}{4}$$

Begin: $$\frac{5}{4}=>$$END Year 2: ($$\frac{5}{4}*\frac{5}{4})=\frac{25}{16}$$

Begin: $$\frac{25}{16}=>$$END Year 3: $$(\frac{25}{16}*\frac{5}{4})=\frac{125}{64}$$

$$125$$ is just about double $$64$$

One more year? Check

Begin: $$\frac{125}{64}=>$$END Year 4:$$(\frac{125}{64}*\frac{5}{4})=\frac{625}{256}$$

MORE than doubled. (256*2 = 512). Too many years.

End of Year 3 was correct.

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The number of years it would take for the value of an investment to do &nbs [#permalink] 01 Aug 2018, 18:38
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