On one of my older articles History of new car costs and average inflation a commenter said that $1500 would grow to over $3 million in 64 years with just 3% interest. I'm not sure how they did the math or what mistake they made but with 3% interest you'd have $9946 after 64 years. Nowhere near $3 million.
Here is the formula to see how much an investment will grow with a given interest return over multiple years :
Growth rate = ( 1 + [interest rate ] ) ^ # Years
The interest rate is expressed in decimal i.e. 3% interest is .03 So for example if you had 3% interest over 64 years that would make the growth rate :
= (1 + [interest rate ] ) ^ Years
= (1 + .03 ) ^ 64
= 1.03 ^ 64
= 6.631
Once you know the growth rate you can find the future value by multiplying your investment by the growth rate. If you start with $1 then you'd end up with $6.63... $100 would give you $663, etc.
Therefore if you start with $1500 and the growth rate is 6.631 then your investment after 64 years of 3% growth would be $1500 x 6.631 = $9946.50
In Windows operating system you can use the x^y key on the scientific layout of the calculator program. The X^Y key is shown in yellow here :
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