It doesn't matter how much you deposit, the time to double your investment for a given rate of interest is the same whether you deposit 10 cents or 10 million dollars. Use the rule of 72 as a sanity check -- 72 divided by the interest rate in percent is the approximate time to double your investment.
And we want
Therefore we need to find the value of that makes when , so
Take the natural log of both sides:
Log of an argument raised to a power is the power times the log of the argument.
But , so
Just use your calculator
Super-Double-Plus Extra Credit. How long to triple your money?
