Question

n 1982 the inflation rate hit 16%. Suppose that the average cost of a textbook in 1982 was $25. What was the expected cost in the year 2017 if we project this rate of inflation on the cost? (Assume continuous compounding. Round your answer to the nearest cent.) If the average cost of a textbook in 2012 was $150, what is the actual inflation rate (rounded to the nearest tenth percent)?

Answer 1

Total number of years = 35

a. Expected cost in 2017 = $25 * e^(35*0.16)

Expected cost in 2017 = $25 * e^5.6

Expected cost in 2017 = $25 * 270.42

Expected cost in 2017 = $6,760.50

b. If the average cost of a textbook in 2012 was $150, then the actual inflation rate:

150 = 25 * e^(r*t)

150 = 25 * e^(r*30)

6 = e^(r*30)

Taking log base e on both side

30r = Ln6

30r = 1.7918

r = 1.7918/30

r = 0.05972667

r = 5.97%

So, actual inflation rate is 5.97%