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The number of years it would take for the value of an invest
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30 Jul 2018, 09:43
30 Jul 2018, 09:43
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Question Stats:
71% (01:19) correct
28% (01:35) wrong based on 57 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
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Re: The number of years it would take for the value of an invest
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11 Aug 2018, 13:35
11 Aug 2018, 13:35
2
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.
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.
Re: The number of years it would take for the value of an invest
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12 Aug 2018, 07:12
12 Aug 2018, 07:12
1
1
Expert Reply
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.
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.
