# Algebra and Trigonometry and Their Applications

#### Math 148 Autumn Quarter, 2001

**Instructor:** *Sergei Chmutov*

Bonus problem. The Rule of 72

The rule of 72
allows you to find the number of years required to double your money at a
given interest rate compounded annually. See the site
"Why it
works"
for a kind of mathematical explanation and for "The rule of 69" for
continuously compounded interest.

Problem:

Find (and provide an explanation) for the similar rules
for interest compounded

**(a)** semiannually
**(b)** quarterly
**(c)** monthly
**(d)** daily

(Answers should be accurate to three decimal places.)