Greatest Balance After 8 Years: Compounded Interest Homework

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In summary, the options to earn the greatest balance after 8 years are: -$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.
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imull
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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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  • #2
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.
 
  • #3
Okay. I was sort of thinking that, but I wanted to be completely sure. Many thanks!
 

Related to Greatest Balance After 8 Years: Compounded Interest Homework

1. What is compounded interest?

Compounded interest is a method of calculating interest where the interest earned in a given period is added to the principal amount, and then the next period's interest is calculated based on the new total. This results in the interest compounding or growing over time.

2. How is compounded interest calculated?

The formula for calculating compounded interest is A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

3. What is the difference between simple interest and compounded interest?

Simple interest is calculated only on the principal amount, while compounded interest takes into account the interest earned in previous periods. This means that compounded interest will result in a higher final amount compared to simple interest.

4. Can compounded interest be negative?

No, compounded interest cannot be negative. This is because the interest rate is always a positive number, and even if the principal amount decreases, the interest earned in previous periods will still be added to the new principal.

5. How long does it take for compounded interest to significantly increase the initial investment?

The time it takes for compounded interest to significantly increase the initial investment depends on the interest rate, the compounding frequency, and the initial amount invested. Generally, the higher the interest rate and the more frequent the compounding, the faster the investment will grow.

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