Identify the variable which fell between the years 2012 and 2015.

The table shows the rate of inflation for a country from 2012 to 2015.
In 2012, the inflation rate was 5.0%.
In 2015, the inflation rate was 3.0%.
The rate of inflation fell from 5.0% to 3.0% over this period. This situation, where the inflation rate decreases but remains positive, is called disinflation.

• B. Average prices: Since the inflation rate is positive in all years (5.0%, 4.0%, 3.5%, 3.0%), it means that average prices are still rising. They are rising at a slower rate, but they are not falling. Therefore, option B is incorrect.
• C. Cost of living: The cost of living is directly related to average prices. As average prices are still rising, the cost of living is also still increasing, not falling. Therefore, option C is incorrect.
• D. The exchange rate: The table provides no information about the exchange rate, and its movement cannot be definitively determined solely from the domestic inflation rate data. Therefore, option D is incorrect.
• A. The value of money: Inflation means that the purchasing power (value) of money is decreasing. When the rate of inflation falls (disinflation), it means that money is still losing value, but it is losing value at a slower rate. In other words, the rate of fall of the value of money has decreased. The magnitude of the annual decrease in the value of money fell from 5% to 3%. This is the most accurate interpretation among the given choices.

The variable which fell between 2012 and 2015 is the rate of inflation. Among the given options, the most appropriate answer, considering the effect of a falling inflation rate, is the rate of fall of the value of money.

The final answer is $\boxed{\text{A}}$