P(1+12) Calculate P1 Calculate = =. Let R = A В' and call this number A. (Round to two decimal places as needed.) (1/2)^ and call this number B. 12 (Round to two decimal places as needed.)
P(1+12) Calculate P1 Calculate = =. Let R = A В' and call this number A. (Round to two decimal places as needed.) (1/2)^ and call this number B. 12 (Round to two decimal places as needed.)
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
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Question

![### Loan Repayment Calculation
**Given Data:**
- **Amount (P):** $160,000
- **Annual Interest Rate (r):** 8%
- **Time (T):** 15 years
We need to find the monthly payment \( R \) necessary to pay off the loan by completing parts a through c. Represent the number of monthly payments by \( n \).
#### Calculation Steps:
1. **Step 1: Calculate Part A**
Calculate \( P \left(1 + \frac{r}{12}\right)^n \) and call this number **A**.
\[
A = \underbrace{\_\_\_\_\_\_\_\_\_\_\_\_}_{\text{Insert calculation here}} \quad \text{(Round to two decimal places as needed.)}
\]
2. **Step 2: Calculate Part B**
Calculate \( \frac{\left(1 + \frac{r}{12}\right)^n - 1}{\frac{r}{12}} \) and call this number **B**.
\[
B = \underbrace{\_\_\_\_\_\_\_\_\_\_\_\_}_{\text{Insert calculation here}} \quad \text{(Round to two decimal places as needed.)}
\]
3. **Step 3: Calculate the Monthly Payment \( R \)**
Let \( R = \frac{A}{B} \).
The monthly payment necessary to pay off the loan is \( R = \$\_\_\_\_\_\_\_\_\_ \).
---
### Note:
- Ensure all calculations are rounded to two decimal places as necessary.
- Final monthly payment \( R \) should be rounded up to the nearest cent for accuracy.
This exercise assists in understanding the mathematical underpinnings of loan repayments, useful for academic purposes and practical financial literacy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe34d490e-1bcd-4b3c-8858-e89cb8d5c9df%2Fd1fd0028-f243-495c-89e7-900fce63696b%2F29kduz9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Loan Repayment Calculation
**Given Data:**
- **Amount (P):** $160,000
- **Annual Interest Rate (r):** 8%
- **Time (T):** 15 years
We need to find the monthly payment \( R \) necessary to pay off the loan by completing parts a through c. Represent the number of monthly payments by \( n \).
#### Calculation Steps:
1. **Step 1: Calculate Part A**
Calculate \( P \left(1 + \frac{r}{12}\right)^n \) and call this number **A**.
\[
A = \underbrace{\_\_\_\_\_\_\_\_\_\_\_\_}_{\text{Insert calculation here}} \quad \text{(Round to two decimal places as needed.)}
\]
2. **Step 2: Calculate Part B**
Calculate \( \frac{\left(1 + \frac{r}{12}\right)^n - 1}{\frac{r}{12}} \) and call this number **B**.
\[
B = \underbrace{\_\_\_\_\_\_\_\_\_\_\_\_}_{\text{Insert calculation here}} \quad \text{(Round to two decimal places as needed.)}
\]
3. **Step 3: Calculate the Monthly Payment \( R \)**
Let \( R = \frac{A}{B} \).
The monthly payment necessary to pay off the loan is \( R = \$\_\_\_\_\_\_\_\_\_ \).
---
### Note:
- Ensure all calculations are rounded to two decimal places as necessary.
- Final monthly payment \( R \) should be rounded up to the nearest cent for accuracy.
This exercise assists in understanding the mathematical underpinnings of loan repayments, useful for academic purposes and practical financial literacy.
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