Rule of 72 - How long does it take to double your money ?

Ok, so now we are feeling pretty good about ourselves since we remember something about compound interest. But are simple calculator next to our check book does NOT do exponential equations. So we go back to simple interest. Shame on you. Are you planning on using hot oil to pop your next batch of popcorn ? Hell no, you are going to NUKE IT in the microwave. So get yourself a real calculator (solar power of course) so you can do some compound interest, and soon i will teach you logs.

It took me thirteen (yes, that is 13) to understand logs, so i am not going to try to explain to you the Law of Logs (LOL) in one blog.

My tutoree today called it "Lots of Luck". I told you he had a high social IQ.

So you will just have to do what i do !!

Lets say you want to know what 5^x = 2.

Algebra is NOT going to help you here. You can do trial and error like they did before the 1800's.

5^1=5, so the answer is less than 1.
5^.5 =5^(1/2)= square root of 5 = 2.24....getting closer.
How about 5^.4 = 1.9...a little low, but closer

Anyways the way we do it in math:
we say we "take the log of both sides"...(just like in algebra we take the square root of both sides of an equation sometimes)

So log 5^x = log 2.

Now we use the Law of Logs (LOL) and we are allowed to bring the "x" up front.

x log 5 = log 2

Finally we divide both sides by log 5

and our answer is x = (log 2) / (log 5) = .43....so 5^(.43) = 2 !!

So you might say WHO CARES ?? just give them the credit card...lol (laugh out loud)

Now how do we double our money ? (the Ben Franklin way !!)

Remember that that compounded continuously we use "Pert shampoo" or A=Pe^(rt)

If we buy a $100 US Bond, believe it or not, it only cost grandma $50 !! (but don't tell the grandkids)...the kids have to wait 20 or 30 years depending on the interest rate the govt is paying before the Bond "matures" or doubles in value up to $100.

So we have $100 = $50 e^(rt)...lets start with 6% interest rate (that was the rate back in the 1980's when things were going well with Ronald Reagan...yes, i had to put that plug in...remember 1989 is when the Russian Empire collapsed and i am a cuban exile...see my other blogs).

So we have $100 = $50 e^(.06 * t). How do we solve this ? with LOGS !!

First get rid of the 50 on both sides.

2 = e^(.06 * t)....(if you can not follow this step, ask you wife or your kids)

now we "take the logs of both sides", but here since the base is e, it will have to be log base e which we call natural log....or "ln"...you will find the button on your calculator (the new one you bought at Walmart for $5.95 that does more than just add and multiply or borrow the one your kids use in school)

ln 2 = ln e^(.06 * t)

using the LOL (Law of Logs) we are allowed to bring the (.06 * t) up front

ln 2 = (.06 * t) ln e

now take my word for it...the ln e = 1

so we have

ln 2 = (.06 * t)

and now we can divide both sides by .06

and we get our final answer.... (ln 2) / .06 = t = 11.5 years

It will take 11.5 years for your money to double at a rate of 6% compounded continuously.

Now we come to the "Rule of 72"

In the business world, if you want a good approximation for when your money will double at 6%, all you have to do is to divide 72 by 6 and you get about 12 years !!

At 3%, it would take 72/3 = about 24 years (this was the rate in the 1990's)

At 2%, it would take 72/2 = about 36 years (this is the rate in the 2000's)

in 2010, it is probably about 1%, or it would take 72 years to double...only the Chinese would buy such cheap stock or bonds....lol

(For the more advance math students, the Rule of 72 should really be the Rule of 70, since the ln 2 is closer to .70 then to .72, but the business world uses 72 ,because MORE numbers go into 72..2,3,4,6,8,9,12....and that keeps me awake at night.)