Homework: Section 5.7 Financial Models Practice Score: 0 of 1 pt 5.7.69 10 of 10

Question

Homework: Section 5.7 Financial Models Practice Score: 0 of 1 pt 5.7.69 10 of 10 (8 HW Score: 50%, 5 of 10 pts The Consumer Price Index (CPI) indicates the relative r% over n years, ten the CPI ater n years is CP.C%) 1. (a) The CPI was 150 5 for 1995 and 173 8 for 1998. Assuming that annual infiation remained constant for this sime period, determine the average annual infation rate 100where CPh is the CPl index at the begihning of the n-year period b) Using the intation rate from part (a), in what year willthe CPI reach 2947 a) The average annual inflation rate from 1995 to 1998 was approximately Div (Round to two decimal places as needed.) 1 pata nine mmmmm

Explanation / Answer

(a)

in 1995 CPI was 150.5

CPIo =150.5

in 1998 , n =1998-1195=3 . CPI was 173.8

=>150.5[1+(r/100)]3=173.8

=>[1+(r/100)]3=(173.8/150.5)

=>1+(r/100)=(173.8/150.5)1/3

=>(r/100)=[(173.8/150.5)1/3-1]

=>r=[(173.8/150.5)1/3-1]*100

=>r=4.9150416542939313972019666982978

=>r=4.92

the average annual inflation rate from 1995 to 1998 was approximately 4.92 %

(b)

CPI =294

=>150.5[1+(4.9150416542939313972019666982978/100)]n=294

=>[1+(4.9150416542939313972019666982978/100)]n=294/150.5

=>1.049150416542939313972019666983n=(294/150.5)

=>n =ln(294/150.5)/ln(1.049150416542939313972019666983)

=>n =13.955956247114035669094892706742

year is 1995+13

year is 2008

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