Question

The consumer price index (CPI) for a given year is the amount of money in that year that has the same purchasing power as $100 in 1983. At the start of 2015, the CPI was 234.1 Write a formula for the CPI as a function of t years after 2015, assuming that the CPI increases by 2.9% every year.

Answer 1

Answer:

The formula should be 234.1 x (1 + 2.9%)^t

Explanation:

As the questions indicates, the CPI indicates what the value for money is in that given year compared to the base year. So a higher CPI amount is given as a result of inflation over the years. So the rate of inflation was such that the 100 dollars in 1983 (taken as the base year) is equivalent to 234.1 in 2015 as a result of inflation. So, essentially, the time value of money concept is being applied here. We can use the formula for calculating the future value of money over here as well.

The equation is: FV = PV × (1 + x%)^t

where, FV is future value, PV is the present value today, x% is the rate of change, and t is the time period in years.

With the values at hand, the formula to compute what the CPI should be t years after 2015,

CPI (t years after 2015) = 234.1 x (1.029)^t