Inflation causes things to cost more and for our money to buy less hence your grandparents saying in my day, you could buy a couple coffee coffee for a nickel suppose inflation decreases the value of the money by 2% each year and other words if you have a dollar this year next year, it will only buy you 0. $.98 worth of things will $100 buy you in 15 years.

To solve this problem, we need to account for the effect of inflation over 15 years. The value of money decreases by 2% each year, meaning the remaining value of money each year is $98\%$ of the previous year’s value. This is an example of exponential decay, which can be modeled using the formula:

\[
V = P \times (1 - r)^t
\]

Where:
- $ V $ is the value of the money after $ t $ years,
- $ P $ is the initial amount of money (in this case, $100),
- $ r $ is the rate of inflation (2%, or 0.02),
- $ t $ is the number of years (15 years).

Plugging in the values:

\[
V = 100 \times (1 - 0.02)^{15}
\]
\[
V = 100 \times (0.98)^{15}
\]

Let’s calculate that.After 15 years of 2% annual inflation, $100 will be worth approximately **$73.86** in terms of purchasing power.

Would you like more details or have any questions on this?

Here are some related questions:
1. How much would $500 be worth after 20 years with the same inflation rate?
2. If inflation were 3% instead of 2%, how much would $100 be worth in 15 years?
3. How long would it take for $100 to lose half its value at a 2% inflation rate?
4. What formula could you use to estimate future purchasing power in real-world scenarios?
5. How does inflation differ from other economic factors like interest rates?

**Tip:** Inflation compounds over time, so even small changes in the inflation rate can significantly affect long-term purchasing power.

Inflation causes things to cost more and for our money to buy less. Suppose inflation decreases the value of money by 2% each year. If you have $100 today, what will it be worth in 15 years?

Learn how to calculate the future value of $100 after 15 years of 2% annual inflation. Using exponential decay, the remaining value of money decreases by 2% each year. This problem covers key concepts such as exponential decay and percentage decrease, ideal for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation