In 1936 a modest cottage on the south shore of Lake Mitchell (near Cadillac) was purchased for $2500. Aside from improved (partial) heating, better access to electricity, and indoor plumbing, the...

In 1936 a modest cottage on the south shore of Lake Mitchell (near Cadillac) was purchased for $2500.  Aside from improved (partial) heating, better access to electricity, and indoor plumbing, the cottage has changed very little since 1936.   However, its value had increased to an estimated $250,000 in 2018.  Use the Compound Interest Formula to help answer the following questions.  You may assume
annual compounding.

1. What is the average annual percentage rate of increase in the value of this cottage from 1936-2018? (Round your answer to the nearest hundredth of a percent.)


2. Using your answer to a), in what year will the cottage be worth $1,000,000?

The
Consumer Price Index, or
CPI, can be described as a number that measures the change in prices that U.S. consumers pay for everyday goods and services.  Simply put, when the CPI goes up, it means that overall consumer prices have gone up (inflation), and when it goes down, overall consumer prices have gone down (deflation).  The CPI has been carefully measured and recorded since 1913.  For a more detailed explanation and a table that gives the CPI, month-by month and annually from 1913-2020, visit

https://inflationdata.com/Inflation/Consumer_Price_Index/HistoricalCPI.aspx?reloaded=true  .      The right-most column, headed AVE. , is the CPI number for the entire year.  Use this                                                  column to help answer the following questions.

1. What was the CPI for 1936? For 2018?


2. What is the average annual percentage rate of increase in the CPI from 1936-2018? (Round your answer to the nearest hundredth of a percent.)


3. What is the difference between your answers to 3a) and 3d)? Does this seem like a big difference?


4. If you use the 1936 purchase price, your answer to 3d), and the Compound Interest Formula, what would the value of the cottage have been in 2018? Does this seem like a big difference compared to its actual value in 2018?