Show that the "doubling time" $($time for your money to double$)$ is $n$ periods at interest rate $i\%$ per period with $ni=69,$ approximately. Show that the error in the approximation is less than $10\%$ if $i\%20\%.($Note that $n$ does not have to be the number of years; it can be the number of months with $i=$ interest rate per month, etc.$)$ Hint: You want $(1+\frac{i}{100}{)}^n=2$; take $ln$ of both sides of this equation and use equation $(13\mathrm{.}4).$ Also see theorem $(14\mathrm{.}3).$