Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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b. What is the total interest?
![**Car Loan Payment Calculation Example**
Suppose that you decide to buy a car for $31,635, including taxes and license fees. You saved $8,000 for a down payment and can get a three-year car loan at 7.59%.
To find the monthly payment and the total interest for the loan, use the formula:
\[
\text{PMT} = \frac{P \left(\frac{r}{n}\right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]
Where:
- \( P \) is the principal amount (loan amount after down payment)
- \( r \) is the annual interest rate (decimal)
- \( n \) is the number of payments per year
- \( t \) is the time in years
**Calculations:**
1. Determine the loan amount (Principal):
- \( P = \text{Total Cost} - \text{Down Payment} = 31,635 - 8,000 = 23,635 \)
2. Use the given interest rate and terms:
- \( r = 0.0759 \) (7.59% annual interest rate)
- \( n = 12 \) (monthly payments)
- \( t = 3 \) (three-year loan)
The monthly payment is calculated using the provided formula.
The monthly payment is displayed as $_____. (Round to the nearest cent as needed.)](https://content.bartleby.com/qna-images/question/dfb3c0e4-4cb8-407e-b5ef-14f8cfdff4c1/6c4344db-beaf-42ec-8a8d-6589c7f1e856/iu20d1n_processed.jpeg)
Transcribed Image Text:**Car Loan Payment Calculation Example**
Suppose that you decide to buy a car for $31,635, including taxes and license fees. You saved $8,000 for a down payment and can get a three-year car loan at 7.59%.
To find the monthly payment and the total interest for the loan, use the formula:
\[
\text{PMT} = \frac{P \left(\frac{r}{n}\right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]
Where:
- \( P \) is the principal amount (loan amount after down payment)
- \( r \) is the annual interest rate (decimal)
- \( n \) is the number of payments per year
- \( t \) is the time in years
**Calculations:**
1. Determine the loan amount (Principal):
- \( P = \text{Total Cost} - \text{Down Payment} = 31,635 - 8,000 = 23,635 \)
2. Use the given interest rate and terms:
- \( r = 0.0759 \) (7.59% annual interest rate)
- \( n = 12 \) (monthly payments)
- \( t = 3 \) (three-year loan)
The monthly payment is calculated using the provided formula.
The monthly payment is displayed as $_____. (Round to the nearest cent as needed.)
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