Today Puzzle #540
Puzzle No. 540 鈥� Wednesday 7 August
In a land very far away the annual rate of inflation is 1 million percent. Assuming there are 365 days in a year what is the daily rate of inflation?
Today’s #PuzzleForToday has been set by David Hargreaves, Visiting Lecturer, Faculty of Actuarial Science and Insurance, Cass Business School
Click here for the answer
Let x be the unknown daily rate of inflation (as a percentage). Then each day the cost of an item will go up by a factor of 1+(x/100) compared with the day before. After 365 days the cost of the item will have gone up by a factor of [1+(x/100)]^365. We therefore have
[1+(x/100)]^365=1+(10^6)/100
Take logs to base 10. Then 365 log[1+(x/100)]=4.000043
This leads to x=2.56 (to 2 decimal places).
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