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# What is factor of 16?

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Manager
Joined: 28 Jun 2009
Posts: 51
Location: Moscow Russia
Schools: -=! LBS (int) !=- HEC (admitted) INSEAD (int)
What is factor of 16? [#permalink]

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03 Aug 2009, 23:26
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Question Stats:

25% (00:01) correct 75% (00:26) wrong based on 11 sessions

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A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

What do they want?

Is t by 16% or 16 times more?

I don't get the idea!

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Manager
Joined: 24 Apr 2009
Posts: 91
Re: What is factor of 16? [#permalink]

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04 Aug 2009, 03:20
A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

What do they want?

Is t by 16% or 16 times more?

I don't get the idea!

the interest is 16 times more..
16 = (1+8/400)^(4x) this would be the correct equation.
take the 4th root on both the side and u'll get B as the answer..
Manager
Joined: 29 Jul 2009
Posts: 112
Re: What is factor of 16? [#permalink]

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04 Aug 2009, 03:46
A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

What do they want?

Is t by 16% or 16 times more?

I don't get the idea!

Well the question stem tells us that if P is the principal amount and if A is the final amount ( along with interest money) ... then factor of 16 means

A = 16P

u can finally sustitute the value in the compund interest formula A=P (1 + ( R/ (100 * x ) ) ^ (n*x)

r=rate of interest
x= number of times compunding is done annually
n= number of years

The calculation is very well explained by atomy.....atomy has just interchanged variables x for n..rest is the same

hth

Last edited by apoorvasrivastva on 04 Aug 2009, 03:57, edited 1 time in total.
Intern
Joined: 01 Aug 2009
Posts: 29
Location: Australia
Re: What is factor of 16? [#permalink]

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04 Aug 2009, 03:51
atomy is right.

The "idea" of the question is to increase the investment (principle) by 16 times.
So, in A = P(1+r/n)^nt, if the initial investment is P then the question wants A = 16P when 8% rate is compounded quarterly over x years.
Therefore, our equation becomes...
16P = P(1+.08/4)^4x => 16 = (1+.08/4)^4x => 2^4 = (1.02)^4x => 2 = (1.02)^x (which is B)
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Senior Manager
Joined: 17 Jul 2009
Posts: 277
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Re: What is factor of 16? [#permalink]

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04 Aug 2009, 07:58
note how the question asks for INCREASE by a factor of 16? does that mean the sum need to be 16 times MORE than the original? so shouldn't this be 17 instead of 16 as the final sum?

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: What is factor of 16?   [#permalink] 04 Aug 2009, 07:58
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# What is factor of 16?

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