
Raaghav G. answered 07/01/19
UC Berkeley student with a 35 in ACT Math
Since the number is a bit confusing, I will assume you meant that monthly prices increase at a rate of 22%. If the number is 2.2%, the same process can be applied with different numbers.
Let initial price be 100. Therefore, the price after 1 month is 122
∴ The ratio of initial price and price after one month is r=122/100=1.22. Since prices are increasing by 22% every month, we can assume that the monthly prices are a geometric progression with the first term as 122.
After 12 months the price will be a1⋅r(n - 1) = 122⋅(1.22)12−1=122⋅(1.22)11≈ 1087.22 (2dp)
So yearly price rise is 1087.22 − 100 = 987.22
Hence yearly price rise in percentage is 987.22 ⋅ 100 = 987.22%
Like I said earlier, if the number is 2.2% monthly increase, the yearly price rise can be calculated with a1⋅r(n - 1) = 102.2⋅(1.022)12−1
All the best!