Question

How long will it take for prices in the economy to double at a 6% annual inflation rate? Round to the nearest hundredth.

Answer 1

Suppose the price today is 100.
In one year, that'll be 106, which is 100 * 1.06.
The next year, it'll be 6% up again, which is 106 * 1.06 = 112.36
The next year after that, it'll be 6% up again, which is (106 * 1.06) * 1.06 = 112.36 * 1.06 = 119.10.

You seeing a pattern here yet?

For year x, the price will be
100 * 1.06^x.
Let that sink in for a minute.

The multiplier of prices is 1.06 to the power of the number of years.

You want to know when the multiplier will be exactly 2, so you need to set:

2 = 1.06^x

You can do this by logs:

ln(2) = ln(1.06)*x
(x) = ln(2)/ln(1.06)

Answer 2

Thank you! I am so glad you are back!

Answer 3

So I keep going until I double the cost of 100 to find out how many years?

Answer 4

Only back for a few minutes. Then I have to go help a grown-up whose "homework" is even harder than yours. :-)