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# A certain investment grows at an annual interest rate of 8%,

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Manager
Joined: 19 Aug 2007
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A certain investment grows at an annual interest rate of 8%, [#permalink]  30 Oct 2007, 11:34
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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)
Manager
Joined: 19 Aug 2007
Posts: 170
Followers: 1

Kudos [?]: 17 [0], given: 0

i dont konw the OA yet, I will get it as soon as i finish this exam and get my results. ill post it then.
VP
Joined: 09 Jul 2007
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Location: London
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Re: PS compounded interest rate [#permalink]  30 Oct 2007, 11:53
jimjohn wrote:
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)

A.
formula:FV=PV(1+r)^n
quarterly: r=interest rate/4
time period: n=4x

FV=PV*16
so
16=(1+0.08/4)^4x
16=(1.02)^4x
Manager
Joined: 19 Aug 2007
Posts: 170
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Kudos [?]: 17 [0], given: 0

ravshonbek thats what i thought too but its not given in the answer choices.
A says ^(x/4) not ^(4x)
Director
Joined: 11 Jun 2007
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Re: PS compounded interest rate [#permalink]  30 Oct 2007, 12:00
Ravshonbek wrote:
jimjohn wrote:
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)

A.
formula:FV=PV(1+r)^n
quarterly: r=interest rate/4
time period: n=4x

FV=PV*16
so
16=(1+0.08/4)^4x
16=(1.02)^4x

i think you set it up correctly.. your answer does not equal to A. shouldn't it be taking sqrt 4 on both sides?

(16)^1/4 =(1.02)^4x *1/4
2 = (1.02)^x
so B
VP
Joined: 09 Jul 2007
Posts: 1108
Location: London
Followers: 6

Kudos [?]: 74 [0], given: 0

jimjohn wrote:
ravshonbek thats what i thought too but its not given in the answer choices.
A says ^(x/4) not ^(4x)

2^4=(1.02)^4x
take squareroot of 4

so

2=(1.02)^x
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