You want to buy a new sports car from Muscle Motors for $79,000. The contract is in the form of a 48-month annuity due at an APR of 7.3 percent. What will your monthly payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Monthly payment
You want to buy a new sports car from Muscle Motors for $79,000. The contract is in the form of a 48-month annuity due at an APR of 7.3 percent. What will your monthly payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Monthly 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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![**Monthly Payment Calculation for a New Sports Car**
You are interested in purchasing a new sports car from Muscle Motors for a total cost of $79,000. The payment contract is structured as a 48-month annuity due at an annual percentage rate (APR) of 7.3 percent. This scenario requires you to determine the monthly payment.
### Steps to Calculate Monthly Payment:
1. **Understand the Scenario:**
- **Principal Amount (PV):** $79,000
- **Annual Percentage Rate (APR):** 7.3%
- **Number of Months (N):** 48 (4 years)
2. **Monthly Interest Rate:**
- Since the APR is 7.3%, to find the monthly interest rate, divide the APR by 12.
- Monthly Interest Rate (I) = \( \frac{7.3\%}{12 months} \)
3. **Annuity Due Formula:**
- The formula to calculate the monthly payment for an annuity due is:
\[
PMT = PV \times \frac{i(1 + i)^n}{(1 + i)^n - 1}
\]
- Here, \(i\) is the monthly interest rate and \(n\) is the total number of payments.
4. **Adjust for Annuity Due:**
- Since it's an annuity due, the payment is made at the beginning of the period. Therefore, adjust the formula accordingly.
### Calculation Requirement:
- **Intermediate Calculations:**
- Do not round intermediate calculations to ensure precision.
- Round the final monthly payment to two decimal places (e.g., 321.16).
Please enter the calculated monthly payment in the provided textbox.
\[ \boxed{\text{Monthly payment: } \underline{\hspace{4cm}}} \]
---
**Note:** Detailed step-by-step guidance, along with formulas, is crucial to ensure students understand each part of the calculation process. This example shows a practical application of financial mathematics in calculating annuity payments for a loan.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd87d8eee-b792-430e-98e8-ed118dd425ec%2F8cbbd435-2b1f-4ab8-ac6e-b5ace240de97%2Fug2pjj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Monthly Payment Calculation for a New Sports Car**
You are interested in purchasing a new sports car from Muscle Motors for a total cost of $79,000. The payment contract is structured as a 48-month annuity due at an annual percentage rate (APR) of 7.3 percent. This scenario requires you to determine the monthly payment.
### Steps to Calculate Monthly Payment:
1. **Understand the Scenario:**
- **Principal Amount (PV):** $79,000
- **Annual Percentage Rate (APR):** 7.3%
- **Number of Months (N):** 48 (4 years)
2. **Monthly Interest Rate:**
- Since the APR is 7.3%, to find the monthly interest rate, divide the APR by 12.
- Monthly Interest Rate (I) = \( \frac{7.3\%}{12 months} \)
3. **Annuity Due Formula:**
- The formula to calculate the monthly payment for an annuity due is:
\[
PMT = PV \times \frac{i(1 + i)^n}{(1 + i)^n - 1}
\]
- Here, \(i\) is the monthly interest rate and \(n\) is the total number of payments.
4. **Adjust for Annuity Due:**
- Since it's an annuity due, the payment is made at the beginning of the period. Therefore, adjust the formula accordingly.
### Calculation Requirement:
- **Intermediate Calculations:**
- Do not round intermediate calculations to ensure precision.
- Round the final monthly payment to two decimal places (e.g., 321.16).
Please enter the calculated monthly payment in the provided textbox.
\[ \boxed{\text{Monthly payment: } \underline{\hspace{4cm}}} \]
---
**Note:** Detailed step-by-step guidance, along with formulas, is crucial to ensure students understand each part of the calculation process. This example shows a practical application of financial mathematics in calculating annuity payments for a loan.
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