Prescott Bank offers you a five-year loan for $54,000 at an annual interest rate of 7.5 percent. What will your annual loan payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Annual loan payment
Prescott Bank offers you a five-year loan for $54,000 at an annual interest rate of 7.5 percent. What will your annual loan payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Annual loan payment
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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![**Understanding Loan Payments Calculation**
Prescott Bank offers you a five-year loan for $54,000 at an annual interest rate of 7.5 percent. What will your annual loan payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
### **Calculation Method:**
To calculate the annual loan payment for a fixed-rate loan, you can use the formula for an annuity payment:
\[ PMT = \dfrac{P \times r}{1 - (1 + r)^{-n}} \]
where:
- \( PMT \) is the annual payment
- \( P \) is the loan principal ($54,000)
- \( r \) is the annual interest rate (7.5%, or 0.075 in decimal form)
- \( n \) is the number of years (5 years)
The calculation involves:
1. Converting the annual interest rate from a percentage to a decimal by dividing by 100.
2. Plugging in the values of \( P \), \( r \), and \( n \) into the formula.
3. Performing the arithmetic steps to find \( PMT \).
### **Interactive Section:**
**Annual loan payment:**
\[ \boxed{\dfrac{54000 \times 0.075}{1 - (1 + 0.075)^{-5}}} \]
Use a financial calculator or spreadsheet software to compute the exact payment and input your findings in the provided field:
\[ \boxed{ \text{ \_\_\_\_\_} } \]
By following these guidelines, students and learners can accurately determine their annual loan payments while ensuring their calculations adhere to financial standards of precision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4075dd7b-7cf0-4080-a9ab-c20ff4793850%2Fa688942d-3dc5-4fdc-8a4e-dff8ababe371%2Fldytdw8_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Loan Payments Calculation**
Prescott Bank offers you a five-year loan for $54,000 at an annual interest rate of 7.5 percent. What will your annual loan payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
### **Calculation Method:**
To calculate the annual loan payment for a fixed-rate loan, you can use the formula for an annuity payment:
\[ PMT = \dfrac{P \times r}{1 - (1 + r)^{-n}} \]
where:
- \( PMT \) is the annual payment
- \( P \) is the loan principal ($54,000)
- \( r \) is the annual interest rate (7.5%, or 0.075 in decimal form)
- \( n \) is the number of years (5 years)
The calculation involves:
1. Converting the annual interest rate from a percentage to a decimal by dividing by 100.
2. Plugging in the values of \( P \), \( r \), and \( n \) into the formula.
3. Performing the arithmetic steps to find \( PMT \).
### **Interactive Section:**
**Annual loan payment:**
\[ \boxed{\dfrac{54000 \times 0.075}{1 - (1 + 0.075)^{-5}}} \]
Use a financial calculator or spreadsheet software to compute the exact payment and input your findings in the provided field:
\[ \boxed{ \text{ \_\_\_\_\_} } \]
By following these guidelines, students and learners can accurately determine their annual loan payments while ensuring their calculations adhere to financial standards of precision.
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