Time to Double or Triple an InvestmentThe formula $t=\frac{\ln \left(m\right)}{n\ln \left(1+{\displaystyle \frac{r}{n}}\right)}$

can be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year.

(a) How many years will it take to double the value of an IRA that compounds annually at the rate of 12%?

(b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of 6%?

(c) Give a derivation of this formula.

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