Greatest Balance After 8 Years: Compounded Interest Homework

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Homework Statement


Assume that you can earn 6% on an investment, compounded daily. Which of the following options would yield the greatest balance after 8 years?
-$20,000 now
-$30,000 after 8 years
-$8000 now and $20,000 after 4 years
-$9000 now, $9000 after 4 years, and $9000 after 8 years


Homework Equations


A=P(1+r/n)^n

The Attempt at a Solution


I understand how to use the equation, where P is the investment, r is the interest rate, and n is the number of times interest is compounded, but I don't understand the last three choices. What does it mean by "$9000 now, $9000 after 4 years, and $9000 after 8 years"?
 
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imull said:

Homework Statement


Assume that you can earn 6% on an investment, compounded daily. Which of the following options would yield the greatest balance after 8 years?
-$20,000 now
-$30,000 after 8 years
-$8000 now and $20,000 after 4 years
-$9000 now, $9000 after 4 years, and $9000 after 8 years


Homework Equations


A=P(1+r/n)^n

The Attempt at a Solution


I understand how to use the equation, where P is the investment, r is the interest rate, and n is the number of times interest is compounded, but I don't understand the last three choices. What does it mean by "$9000 now, $9000 after 4 years, and $9000 after 8 years"?
You invest $9000 now, you invest another $9000 four years from now, and you invest another $9000 eight years from now.
 
Okay. I was sort of thinking that, but I wanted to be completely sure. Many thanks!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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