Annual Inflation Rate Problem This question has me stumped. Anyone have ideas to point me in the right direction of a quick and easy way to solve this? I took this from a practice GRE subject math test and each problem is only suppose to take 2.5 minutes to solve. **At a 15 percent annual inflation rate, the value of the dollar would decrease by approximately one-half every 5 years. At this inflation rate, how many years would the dollar be worth one millionth of its present value?**

$V$ as initial value of the dollar, decreases approximately one half: $V_{n+1}\approx\frac{1}{2}V_n$ every $5$ years.

$V$ at first.
$\frac{1}{2}V$ after $5$ years.
$\frac{1}{4}V$ after $10$ years.
$\dots$

After $5n$ years:

$$ V\approx\frac{1}{2^{n}}V_0$$

Now for one-millionth solve:

$1/2^n=1/1000000$

$2^n=1000000$

$n\approx19.9316$




Thus the answer is after $\approx100$ years which is a rough rounded estimate.