SOLUTION: Could you please explain how the rule of 72 works. I understand that it is an easy way to figure out how many years it would take to double your money, but I get very confused abo

Question 38464: Could you please explain how the rule of 72 works. I understand that it is an easy way to figure out how many years it would take to double your money, but I get very confused about why it works. How do I use a logrithm to solve it? I just don't understand logs at all. I know that they are exponents, right? I'm lost
Found 2 solutions by stanbon, Nate:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If P amount of money is compounded continuously the
amount (A) of money you will get is as follows:
A=Pe^rt where r is the annual interest rate and t is the number
of years you allow the compounded to go on.
Your problem is to find "t" so that A will equal 2P, i.e.
P will double.
So, 2P=Pe^rt
Divide both sides by P to get;
2 =e^rt
Take the natural logarithm of both sides to get
ln2 = rt
t = (1/r)ln2= (1/r)(0.69314718...)
If t = 7 then
r=0.69314718...
r is approximately 10%
All of this says that money will double in value
every 7 years if invested in a continuously
compounding account at 10% annual interest.
Cheers,
Stan H.

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Another way to express total amount with interest compouned continously is:
where P(a) is the total amount, 'a' is the initial amount, 'r' is the rate, 't' is the time in years
Now, if your rate is 4% per year, than you get one whole value of the initial amount with the 4% of the initial amount per year.
Let us say you save $10 for 2 years with 4%

You would get about eighty two cents for the two years. Add the initial amount to get the total amount. Also, I have a lesson about logarithms that can help you.
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