Question

The Consumer Price Index is maintained by an agency of our federal government and is a tool we use to track inflation. The Consumer Price Index was 35.5 at the end of 1968 and 251.2 at the end of 2018, which means that the same goods and services which cost $35.50 at the end of 1968 cost $251.20 at the end of 2018. a. The Dow Jones Industrial Average stood at 943.75 at the end of 1968. Assuming the Dow Jones Industrial Average increased at the same rate as the Consumer Price Index, at what level should the Dow Jones Industrial Average have stood at the end of 2018? b. The Dow Jones Industrial Average stood at 23,327.46 at the end of 2018. If you invested in a stock fund tied to the Dow Jones Industrial Average at the end of 1968, is the buying power of your investment now more than it was in 1968, about the same as it was in 1968, or less than it was in 1968?

Answer 1

Year	CPI
1968	35.5
2018	251.2

If r is the annual rate of return, then

=>

The above equation can be solved taking log of both sides.

Solving, we get: r = 3.9912% ~ 4%

DJIA was 943.75 at the end of 1968. Assuming same annual rate of increase, DJIA at then end of 2018 should be

The Dow Jones Industrial Average stood at 23,327.46 at the end of 2018, compared to 6678.03 as determined from the CPI rate of increase. Hence the investment tied to DJIA has more buying power than it had in 1968.