A price index was approximately 97.8 (base year 1992) at the beginning of 1991. If inflation continued at an average annual rate of 2.5%, what would the index be at the beginning of 2021?

By using the compound interest formula, the future value of the price index in 2021, if inflation continued at an annual rate of 2.5% from the base year 1991, would be approximately 209.375.

Explanation:

The subject of the question is Calculating Future Value with continuous compounding in mathematics.

The price index and the annual inflation rate are given, and you are asked to predict the index level after 30 years.

To solve this, we need to use the compound interest formula which is: Future Value = Present Value * (1 + Interest Rate)^Time.

Here, the Present Value is the price index at the beginning of 1991 (which is 97.8), the Interest Rate is the rate of inflation (2.5%, or 0.025 as a decimal), and the Time is the number of years until 2021 (which is 30 years).

So, filling those numbers into the formula, we would get: Future Value = 97.8 * (1 + 0.025)^30

If we calculate this, our final answer is approximately 209.375.

Therefore, if inflation continued at an average annual rate of 2.5%, the price index would be around 209.375 at the beginning of 2021.

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