In​ 1923, a certain country underwent one of the worst periods in history of​ hyperinflation, which is extraordinarily large inflation in prices. At the peak of the​ hyperinflation, prices rose 11,000​% per month. At this​ rate, by what percentage would prices have risen in 1​ year? In 1​ day? (Assume 30 days per​ month.)

The annual inflation rate is ___ x 10 ^ ___​%
​(Type whole​ numbers.)

The daily inflation rate is ___ %.
(Round to the nearest whole number as needed.)

Answer: 3.498 * 10^26 % ; 16.9% per day

Step-by-step explanation:

Inflation rate = 11,000 per month

Hence, price after a month :

Final price = initial price (1 + rate)

Final price = 1 + 11000/100

Final price = (1 + 110) * initial price

Final price = 111 times the initial price

Hence inflation over the 12 month period :

(111)^12 = 3.498 * 10^24

(3.498 * 10^24) * 100% = 3.498 * 10^26 %

The daily inflation rate :

Number of days = 30

30th root of 3.498 * 10^24 = 1.169

(1.169 - 1) = 0.169

0.169 * 100% = 16.9% per day

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