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%.