## 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 :

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#### 3 comments:

1. I did the math on Phillip J Fry becoming a billionaire because of 93 cents he left in his account for 1000 years. To my surprise, their math was correct.

Too bad the same can't be said of your commenter. It would take 256 years to grow \$1500 to \$1 million.

1. Sorry, when I said "\$1 million" I meant "\$3 million".

2. SteveD,

Thumbs up for the Futurama reference. ;) You're right 1000 years would compound nicely. But I expect the 93 cents would have been eaten by fees or handed over to the state as unclaimed assets long before that. :(

Jim

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