Solve for the unknown interest rate in each of the following (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future Value 300 % s 380 1,394 237,520 4 420 18 45,000 19 44,261 25 703,627 %24
Solve for the unknown interest rate in each of the following (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future Value 300 % s 380 1,394 237,520 4 420 18 45,000 19 44,261 25 703,627 %24
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
![### Solving for Unknown Interest Rates
To solve for the unknown interest rate in each scenario, use the time value of money formula for compound interest:
\[ FV = PV \times (1 + r)^n \]
Where:
- \( FV \) is the future value.
- \( PV \) is the present value.
- \( r \) is the interest rate per period.
- \( n \) is the number of periods.
Follow these steps to isolate the interest rate (\( r \)):
1. Rearrange the formula to solve for \( r \):
\[ r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1 \]
2. Plug in the known values for \( FV \), \( PV \), and \( n \).
3. Calculate the interest rate and express it as a percent rounded to 2 decimal places.
**Instructions:**
- Do not round intermediate calculations.
- Enter your answers as a percent rounded to 2 decimal places (e.g., 32.16%).
#### Problem Table
| Present Value ($) | Years (n) | Interest Rate (%) | Future Value ($) |
|--------------------|-----------|-------------------|------------------|
| 300 | 4 | \[ \text{To be calculated} \] | 380 |
| 420 | 18 | \[ \text{To be calculated} \] | 1,394 |
| 45,000 | 19 | \[ \text{To be calculated} \] | 237,520 |
| 44,261 | 25 | \[ \text{To be calculated} \] | 703,627 |
### Example Calculation
For the first row:
- Present Value (\( PV \)) = $300
- Future Value (\( FV \)) = $380
- Number of Years (\( n \)) = 4
- Interest Rate (\( r \)) = ?
Plug the values into the rearranged formula:
\[ r = \left(\frac{380}{300}\right)^{\frac{1}{4}} - 1 \]
Calculate:
\[ r = \left(1.2667\right)^{0.25} - 1 \approx 0.06099 \]
Convert to percent:
\[ r \approx 6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F249e3087-ac84-499e-a043-461bff034fe9%2F24e1d356-5d55-49ef-a8d2-46c9f8330198%2F9hykf0o.png&w=3840&q=75)
Transcribed Image Text:### Solving for Unknown Interest Rates
To solve for the unknown interest rate in each scenario, use the time value of money formula for compound interest:
\[ FV = PV \times (1 + r)^n \]
Where:
- \( FV \) is the future value.
- \( PV \) is the present value.
- \( r \) is the interest rate per period.
- \( n \) is the number of periods.
Follow these steps to isolate the interest rate (\( r \)):
1. Rearrange the formula to solve for \( r \):
\[ r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1 \]
2. Plug in the known values for \( FV \), \( PV \), and \( n \).
3. Calculate the interest rate and express it as a percent rounded to 2 decimal places.
**Instructions:**
- Do not round intermediate calculations.
- Enter your answers as a percent rounded to 2 decimal places (e.g., 32.16%).
#### Problem Table
| Present Value ($) | Years (n) | Interest Rate (%) | Future Value ($) |
|--------------------|-----------|-------------------|------------------|
| 300 | 4 | \[ \text{To be calculated} \] | 380 |
| 420 | 18 | \[ \text{To be calculated} \] | 1,394 |
| 45,000 | 19 | \[ \text{To be calculated} \] | 237,520 |
| 44,261 | 25 | \[ \text{To be calculated} \] | 703,627 |
### Example Calculation
For the first row:
- Present Value (\( PV \)) = $300
- Future Value (\( FV \)) = $380
- Number of Years (\( n \)) = 4
- Interest Rate (\( r \)) = ?
Plug the values into the rearranged formula:
\[ r = \left(\frac{380}{300}\right)^{\frac{1}{4}} - 1 \]
Calculate:
\[ r = \left(1.2667\right)^{0.25} - 1 \approx 0.06099 \]
Convert to percent:
\[ r \approx 6
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Recommended textbooks for you
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education