Investment

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heshamelaziry
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Topic: Investment

Mon Nov 02, 2009 8:29 pm

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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?

OA 2 = (1.02)^x

life is a test
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Mon Nov 02, 2009 11:31 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 2 = (1.02)^x 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.

ssuarezo
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Tue Nov 03, 2009 11:02 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 2 = (1.02)^x 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

NikolayZ
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Wed Nov 04, 2009 3:29 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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Wed Nov 04, 2009 10:04 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 2 = (1.02)^x 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.