Pretend the US inflation rate had been 3.8% per year and the Argentinian inflation rate had been 37% per month.
(a) What is the yearly equivalent of Argentina's 37% monthly inflation rate?
(b) What is the monthly equivalent of the US 3.8% yearly inflation rate?
see "Math - Clarence today at 11:45am"
To calculate the yearly equivalent of Argentina's 37% monthly inflation rate, we need to compound the monthly rate over 12 months.
(a) Yearly equivalent of Argentina's 37% monthly inflation rate:
To calculate the yearly equivalent, we can use the formula:
(1 + r)^n = (1 + i),
where r is the monthly inflation rate, n is the number of months, and i is the equivalent yearly inflation rate we want to find.
In this case, r = 0.37 (37%) and n = 12 (number of months in a year).
(1 + 0.37)^12 = (1 + i)
1.37^12 = (1 + i)
Now solving for i:
i = (1.37^12) - 1
Thus, the yearly equivalent of Argentina's 37% monthly inflation rate is approximately 508.57%.
(b) Monthly equivalent of the US 3.8% yearly inflation rate:
To find the monthly equivalent, we need to solve for the monthly rate that compounds over 12 months to give us a yearly rate of 3.8%.
Using the same formula as above:
(1 + r)^n = (1 + i).
Let's assume the monthly inflation rate we want to find is m.
(1 + m)^12 = (1 + 0.038)
1 + m = (1 + 0.038)^(1/12)
Now solving for m:
m = (1 + 0.038)^(1/12) - 1
Thus, the monthly equivalent of the US 3.8% yearly inflation rate is approximately 0.31%.