College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section: Chapter Questions
Problem 8CC
Related questions
Question
![**Lesson: 4.8 Simple and Compound Interest**
**Question 2 of 9, Step 1 of 1**
---
**Problem Statement:**
What principal would you need to invest at a rate of 7% to earn $150 in 9 months? Round your answer to the nearest cent.
---
**Answer:**
_$_________________________________
---
**Explanation:**
In this problem, you are required to calculate the initial principal you would need to invest at a given interest rate to achieve a specified earning within a certain period.
Here's how you can approach the problem:
1. **Identify known values:**
- Interest earned (\(I\)): $150
- Interest rate (\(r\)): 7% or 0.07 (as a decimal)
- Time period (\(t\)): 9 months
2. **Convert the time period into years:**
- Since the time should be in years for interest calculation, you need to divide 9 months by 12, resulting in 0.75 years.
3. **Use the Simple Interest Formula:**
\[
I = P \times r \times t
\]
where:
- \(I\) is the interest earned,
- \(P\) is the principal amount,
- \(r\) is the annual interest rate,
- \(t\) is the time period in years.
4. **Rearrange the formula to solve for \(P\):**
\[
P = \frac{I}{r \times t}
\]
5. **Substitute the known values into the formula** to find the principal \(P\):
\[
P = \frac{150}{0.07 \times 0.75} = \frac{150}{0.0525}
\]
6. **Compute** the value:
\[
P \approx 2857.14
\]
Therefore, the principal you need to invest is approximately $2857.14.
---
**Progress Indicator:**
A horizontal bar at the top of the page indicates the progress. It shows that 1 question out of 9 has been correctly answered.
---
**Copyright Notice:**
© 2022 Hawkes Learning
---
This method allows you to understand the step-by-step approach to solving problems related to simple interest calculations. Happy learning!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F826729b3-3b3d-4c8b-ab95-848f98a13142%2F9e75cdd9-6ac8-4b21-ae60-95ca7cc86690%2Fz8z6k7w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Lesson: 4.8 Simple and Compound Interest**
**Question 2 of 9, Step 1 of 1**
---
**Problem Statement:**
What principal would you need to invest at a rate of 7% to earn $150 in 9 months? Round your answer to the nearest cent.
---
**Answer:**
_$_________________________________
---
**Explanation:**
In this problem, you are required to calculate the initial principal you would need to invest at a given interest rate to achieve a specified earning within a certain period.
Here's how you can approach the problem:
1. **Identify known values:**
- Interest earned (\(I\)): $150
- Interest rate (\(r\)): 7% or 0.07 (as a decimal)
- Time period (\(t\)): 9 months
2. **Convert the time period into years:**
- Since the time should be in years for interest calculation, you need to divide 9 months by 12, resulting in 0.75 years.
3. **Use the Simple Interest Formula:**
\[
I = P \times r \times t
\]
where:
- \(I\) is the interest earned,
- \(P\) is the principal amount,
- \(r\) is the annual interest rate,
- \(t\) is the time period in years.
4. **Rearrange the formula to solve for \(P\):**
\[
P = \frac{I}{r \times t}
\]
5. **Substitute the known values into the formula** to find the principal \(P\):
\[
P = \frac{150}{0.07 \times 0.75} = \frac{150}{0.0525}
\]
6. **Compute** the value:
\[
P \approx 2857.14
\]
Therefore, the principal you need to invest is approximately $2857.14.
---
**Progress Indicator:**
A horizontal bar at the top of the page indicates the progress. It shows that 1 question out of 9 has been correctly answered.
---
**Copyright Notice:**
© 2022 Hawkes Learning
---
This method allows you to understand the step-by-step approach to solving problems related to simple interest calculations. Happy learning!
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