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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.
c. What annual rate of reth will Keiko earn if she invests today and receives
in 20 years?
% (Round to two decimal places.)

Ask by Ward Johnston. in the United States
Jan 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Keiko earns an annual rate of return of approximately 6.69%.

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The Deep Dive

To determine the annual rate of return for Keiko’s investment, we can use the formula for compound interest:
Where:
  • is the amount of money accumulated after n years, including interest.
  • is the principal amount (the initial investment).
  • is the annual interest rate (decimal).
  • is the number of years the money is invested.
Rearranging this formula to find :
For option ©:
Now plug in the numbers:
Calculating the fraction:
Then, apply the exponent:
Converting this to a percentage and rounding to two decimal places:
So, if Keiko invests today, she will earn an approximate annual rate of return of 8.10% over the next 20 years.

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