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Investment

by heshamelaziry » Mon Nov 02, 2009 7:29 pm
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?

OA [spoiler]2 = (1.02)^x[/spoiler]
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Re: Investment

by life is a test » Mon Nov 02, 2009 10:31 pm
heshamelaziry 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?

OA [spoiler]2 = (1.02)^x[/spoiler]
16=(1 + (0.08/4))^4x -> 16 = 1.02^4x -> taking the 4th root of either side --> 16 ^(1/4)= 1.02^(4x)^(1/4)-> 2=1.02^x

hope that helps.
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Re: Investment

by ssuarezo » Tue Nov 03, 2009 10:02 pm
life is a test wrote:
heshamelaziry 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?

OA [spoiler]2 = (1.02)^x[/spoiler]
16=(1 + (0.08/4))^4x -> 16 = 1.02^4x -> taking the 4th root of either side --> 16 ^(1/4)= 1.02^(4x)^(1/4)-> 2=1.02^x

hope that helps.
LifeTest:

I got lost:
Why (0.08/4)? it's 8% quarterly, but when divided by 4, you get the rate monthly, right?, also, how did u get 4x? I think, it's the number of months, how did u get that number?

Thank you for your patience.
Silvia
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by NikolayZ » Wed Nov 04, 2009 2:29 am
Hey Ssuarezo

Look at the question stem, it says "annual interest rate" compounded quarterly. So, if there are 4 quarters in a year, it must be that the rate per a quarter might be found through division of annual interest rate by 4.
(0.08/4)=0.02
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Re: Investment

by life is a test » Wed Nov 04, 2009 9:04 pm
ssuarezo wrote:
life is a test wrote:
heshamelaziry 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?

OA [spoiler]2 = (1.02)^x[/spoiler]
16=(1 + (0.08/4))^4x -> 16 = 1.02^4x -> taking the 4th root of either side --> 16 ^(1/4)= 1.02^(4x)^(1/4)-> 2=1.02^x

hope that helps.
LifeTest:

I got lost:
Why (0.08/4)? it's 8% quarterly, but when divided by 4, you get the rate monthly, right?, also, how did u get 4x? I think, it's the number of months, how did u get that number?

Thank you for your patience.
Silvia
the 8% is an annual rate, if it is componded quarterly then it will get rolled over 4 times in a year hence 4X and the rate each quarter will be 8%/4.

Hope that helps.
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