If prices increase at a monthly rate of 2 p.2 % by what percentage do they increase in a yearerc

Question

The biannual inflation rate is ?

Answer 1

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!