## January 24, 2013

### How To FIgure How Much An Investment Grows Over TIme with Interest

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 :

-- 