Your grandmother opened an investment account of $1,000(initial deposit) 15 years ago.

Today it's worth $39,533.32

What is average annual rate of return that she earned?

Thank you.

1000(1+r)^15 = 39533.32

(1+r)^15 = 39.53332
1+r = 1.2778
r = 0.2778 = 27.78%

is that a sane answer? yes, since it doubled over 5 times in 15 years, or every 3 years. The rule of 72 says that a rate of 24% will double about every 3 years.

To find the average annual rate of return on an investment, you can use the formula:

Average Annual Rate of Return = (Final Value / Initial Deposit)^(1 / Number of Years) - 1

In this case, the final value is $39,533.32 and the initial deposit is $1,000. The number of years is 15.

Plugging in these values into the formula, we have:

Average Annual Rate of Return = ($39,533.32 / $1,000)^(1 / 15) - 1

Calculating this equation gives us:

Average Annual Rate of Return = (39.53332)^(1 / 15) - 1

Using a calculator, we can evaluate:

Average Annual Rate of Return ≈ 1.0645 - 1

Therefore, the average annual rate of return that your grandmother earned on her investment over the past 15 years is approximately 0.0645 or 6.45%.