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 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 15 years?

The problem can be solved by recognizing that this is a case of exponential decay, where the value of money decreases by 4% each year. The formula for the value of money after a certain time, given a consistent percentage decrease, is:

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

Where:
- $A$ is the amount of money in terms of purchasing power after $t$ years.
- $P$ is the initial amount of money.
- $r$ is the rate of decrease (inflation rate, 4% or 0.04).
- $t$ is the number of years (15 years in this case).

Substitute the values into the formula:

\[
A = 100(1 - 0.04)^{15}
\]
\[
A = 100(0.96)^{15}
\]

Let me calculate this.After 15 years, $100 will have the purchasing power of approximately $54.21, assuming a constant 4% inflation rate each year.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How much would $500 be worth in purchasing power in 20 years under the same inflation rate?
2. What is the inverse of this scenario—how much would you need today to have $100 worth of purchasing power in 15 years?
3. How does compound interest compare with inflation in terms of value growth or decay over time?
4. If inflation varied each year, how would you model the changing value of money?
5. How does inflation impact long-term financial planning and retirement savings?

**Tip**: Understanding inflation helps in making smarter investment decisions, as money loses value over time if it just sits without earning interest.

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 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 15 years?

Find out how to calculate the future value of $100 in purchasing power after 15 years with a consistent 4% inflation rate. Learn about exponential decay and inflation, and apply the formula A = P(1 - r)^t. Suitable for students in 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