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# The number of years it would take for the value of an invest

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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The number of years it would take for the value of an invest [#permalink]  30 Jul 2018, 09:43
Expert's post
00:00

Question Stats:

100% (00:21) correct 0% (00:00) wrong based on 2 sessions
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
[Reveal] Spoiler: OA

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Sandy
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Intern
Joined: 10 Aug 2018
Posts: 33
Followers: 0

Kudos [?]: 12 [0], given: 0

Re: The number of years it would take for the value of an invest [#permalink]  11 Aug 2018, 13:35
Super important to work smart on these questions. With a proper calculator, you would use logarithms to solve this, but as the GRE doesn't allow a proper calculator, you should note that you have an ascending list of numbers, and check first B and then (if necessary) D. If B gives you a value that is too large, your answer is A. If B gives you a value that is too small, you check D. If D gives you a value that is too large, your answer is C. If D gives you a value that is too small, your answer is E.

Let's do it:

1.26^3 = 2.0004.

Here we get lucky and B is your answer. Still, we would only have needed to check one other option had B been incorrect. This method will save you A LOT of time on test day.
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [0], given: 396

Re: The number of years it would take for the value of an invest [#permalink]  12 Aug 2018, 07:12
Expert's post
Explanation

Start with $1, and multiply by $$(1+\frac{26}{100})= 1.26$$ for each year that passes. In order for the amount to double, it would have to reach$2:

End of Year 1: $1 × 1.26 =$1.26

End of Year 2: $1.26 × 1.26 =$1.5876

End of Year 3: $1.5876 × 1.26 =$2.000376 ≈ \$2.00

It takes 3 years for the investment to double in value. In terms of simple interest, it would take about 4 years (since 26% is just a tiny bit more than 25% = 1/4). The compounded case earns “interest on the interest,” though, so the investment grows more quickly.
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Sandy
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Re: The number of years it would take for the value of an invest   [#permalink] 12 Aug 2018, 07:12
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