Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 3% each year. In other words, if you have $1 this year, next year it will only buy you $0.97 worth of stuff. How much will $100 buy you in 20 years?


To determine how much $100 today will buy you in 20 years given an annual 3% decrease in purchasing power, we can use the exponential decay formula:

\[
\text{Future Value} = \text{Present Value} \times (1 - \text{rate})^{\text{years}}
\]

where:
- **Present Value** = $100 (the amount today),
- **rate** = 3%, or 0.03,
- **years** = 20.

### Step 1: Set up the formula
\[
\text{Future Value} = 100 \times (1 - 0.03)^{20}
\]

### Step 2: Simplify inside the parentheses
\[
\text{Future Value} = 100 \times (0.97)^{20}
\]

### Step 3: Calculate $(0.97)^{20}$
Using a calculator, we find:
\[
(0.97)^{20} \approx 0.5434
\]

### Step 4: Calculate the final amount
\[
\text{Future Value} = 100 \times 0.5434 = 54.34
\]

### Conclusion
In 20 years, $100 today will have the purchasing power of **$54.34**.

Would you like more details or have any questions?

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Here are five related questions to explore further:
1. How would the result change if inflation were 5% per year instead?
2. What is the purchasing power after 10 years at a 3% inflation rate?
3. How would compound interest affect the purchasing power if invested?
4. How long would it take for money to lose half its value at 3% inflation?
5. If inflation rates vary, how does that affect long-term purchasing power?

**Tip:** For any problem involving decay, like inflation or depreciation, exponential decay models are often useful to find long-term impacts.

Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying 'In my day, you could buy a cup of coffee for a nickel'). Suppose inflation decreases the value of money by 3% each year. In other words, if you have $1 this year, next year it will only buy you $0.97 worth of stuff. How much will $100 buy you in 20 years?

Learn how to calculate the purchasing power of $100 in 20 years given a 3% annual inflation rate. This example uses the exponential decay formula, covering core concepts such as inflation impact on value and percentage decrease. Suitable for high school students in Grades 9-12.

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