Investment

[heshamelaziry]

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]

[life is a test]

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.

[ssuarezo]

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

[NikolayZ]

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

[life is a test]

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.