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Interest rate (with changing years). Keiko is looking at the following investment choices and wants to
know what annual rate of return each choice produces.
a. Invest and receive in 11 years.
b. Invest and receive in 17 years.
c. Invest and receive in 20 years.
d. Invest and receive in 40 years.
d. What annual rate of return will Keiko earn if she invests today and receives
in 40 years?
(Round to two decimal places.)

Ask by Ramos O'Quinn. in the United States
Jan 22,2025

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Answer

Keiko will earn an annual rate of return of 9.57%.

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Bonus Knowledge

To determine the annual rate of return for Keiko’s investment, we can use the formula for compound interest, which is:
Where:
  • is the amount of money accumulated after n years, including interest.
  • is the principal amount (the initial amount of money).
  • is the annual interest rate (as a decimal).
  • is the number of years the money is invested.
For Keiko’s investment of that grows to over years, we can rearrange the formula to solve for :
  2. Divide both sides by :
  3. Calculate :
  4. Now take the 40th root of both sides to solve for :
  5. Using a calculator, we find: Hence,
Now converting to a percentage:
So, Keiko will earn an annual rate of return of approximately 10.00%.
Delving into the world of investments, it’s essential to understand how powerful compounding can be. Just imagine: if you invest wisely, a little today can turn into a fortune tomorrow! Historically speaking, the stock market has averaged about a 7% return annually over the long haul, which highlights the potential for growth when you allow your money to work for you.
As for practical tips, avoid the common pitfall of making emotional investment decisions! Stick to your plan and closely monitor your investments without allowing panic to dictate your actions. Prepare for market fluctuations so you can stay focused on your long-term goals and reap the benefits of patience!

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