s Compounding If the present value of an item is P and we experience an inflation rate of r for t years, what will the future value of the item be? P = $500 r = 5% t = 20 Round your answer to the nearest cent. Enter
s Compounding If the present value of an item is P and we experience an inflation rate of r for t years, what will the future value of the item be? P = $500 r = 5% t = 20 Round your answer to the nearest cent. Enter
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Inflation and Future Value Calculation
**Problem Statement:**
If the present value of an item is \( P \) and we experience an inflation rate of \( r \) for \( t \) years, what will the future value of the item be?
### Given:
- \( P = \$500 \)
- \( r = 5\% \)
- \( t = 20 \) years
### Instructions:
1. **Understand the Formula:**
The future value \( FV \) after inflation can be calculated using the formula:
\[
FV = P \times (1 + r)^t
\]
Where:
- \( P \) is the present value.
- \( r \) is the inflation rate (expressed as a decimal).
- \( t \) is the number of years.
2. **Convert the Percentage to a Decimal:**
Since \( r = 5\% \), convert it to a decimal by dividing by 100.
\[
r = \frac{5}{100} = 0.05
\]
3. **Substitute the Values:**
\[
FV = 500 \times (1 + 0.05)^{20}
\]
4. **Calculate:**
Perform the calculation step-by-step:
\[
FV = 500 \times (1.05)^{20}
\]
5. **Round the Answer to the Nearest Cent:**
Ensure your final answer is rounded to the nearest cent.
### Submit Your Answer:
Enter your rounded answer below and click "Enter."
---
**Input Box:** `[ ]`
- (Button) Enter
**Note:** Make sure your calculation is precise and double-check the rounding off errors before submission.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1381e7cd-7d9c-4a6c-a869-dc89813452b2%2Fbb64f499-826d-4277-acfe-4b02278ddb7f%2Fk9k894k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Inflation and Future Value Calculation
**Problem Statement:**
If the present value of an item is \( P \) and we experience an inflation rate of \( r \) for \( t \) years, what will the future value of the item be?
### Given:
- \( P = \$500 \)
- \( r = 5\% \)
- \( t = 20 \) years
### Instructions:
1. **Understand the Formula:**
The future value \( FV \) after inflation can be calculated using the formula:
\[
FV = P \times (1 + r)^t
\]
Where:
- \( P \) is the present value.
- \( r \) is the inflation rate (expressed as a decimal).
- \( t \) is the number of years.
2. **Convert the Percentage to a Decimal:**
Since \( r = 5\% \), convert it to a decimal by dividing by 100.
\[
r = \frac{5}{100} = 0.05
\]
3. **Substitute the Values:**
\[
FV = 500 \times (1 + 0.05)^{20}
\]
4. **Calculate:**
Perform the calculation step-by-step:
\[
FV = 500 \times (1.05)^{20}
\]
5. **Round the Answer to the Nearest Cent:**
Ensure your final answer is rounded to the nearest cent.
### Submit Your Answer:
Enter your rounded answer below and click "Enter."
---
**Input Box:** `[ ]`
- (Button) Enter
**Note:** Make sure your calculation is precise and double-check the rounding off errors before submission.
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