SOLUTION: The "rule of 72" says that your money will double when the product of the interest rate and the number of years equals 72. At 4% interest, how many years will it take for $100,000

Question 970723: The "rule of 72" says that your money will double when the product of the interest rate and the number of years equals 72. At 4% interest, how many years will it take for $100,000 to be worth $1.6 million, in years.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
That is 4 doubling times or 18*4=72 years
P=Po e^rt
P=Principal at end
Po=Principal at beginning
P/Po=e^rt
ln (P/Po)=rt
But P=2 Po
ln 2=rt
0.693=rt
69.3%=rt
We round it to 72, because it is divisible by so much more
72/4 years =18 years
In this problem
ln (16)=.04t
t=69.31 years. The rule says 72 years, so that is the answer.
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