Greatest Balance After 8 Years: Compounded Interest Homework

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SUMMARY

The discussion centers on evaluating investment options with a 6% interest rate compounded daily over 8 years. The options analyzed include investing $20,000 now, $30,000 after 8 years, $8,000 now with $20,000 after 4 years, and $9,000 at three different intervals. The formula used for calculations is A=P(1+r/n)^n, where A is the amount after time, P is the principal investment, r is the interest rate, and n is the compounding frequency. The clarification sought pertains to the interpretation of staggered investments, specifically the option of investing $9,000 now, $9,000 after 4 years, and $9,000 after 8 years.

PREREQUISITES
  • Understanding of compound interest and its calculations
  • Familiarity with the formula A=P(1+r/n)^n
  • Basic knowledge of investment strategies
  • Ability to perform financial comparisons between different investment options
NEXT STEPS
  • Calculate the future value of each investment option using A=P(1+r/n)^n
  • Explore the impact of different compounding frequencies on investment returns
  • Research the effects of inflation on investment growth over time
  • Learn about other investment vehicles with varying risk and return profiles
USEFUL FOR

Investors, financial analysts, students studying finance, and anyone interested in understanding the implications of compounded interest on investment choices.

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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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!
 

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