How long will it take for prices in the economy to double at a 6% annual inflation rate? Round to the nearest hundredth.
Thank you! I am so glad you are back!
So I keep going until I double the cost of 100 to find out how many years?
Only back for a few minutes. Then I have to go help a grown-up whose "homework" is even harder than yours. :-)
To calculate how long it will take for prices in the economy to double at a 6% annual inflation rate, we can use the rule of 70. The rule of 70 states that you can approximate the time it takes for a variable to double by dividing 70 by the annual growth rate.
In this case, the annual growth rate is 6%, so we divide 70 by 6 to get an approximation of 11.67.
Therefore, it would take approximately 11.67 years for prices in the economy to double at a 6% annual inflation rate.
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)