Suppose that you decide to borrow $17,000 for a new car. You can select one of the following loans, each requiring regular monthly payments. Installment Loan A: three-year loan at 6.3% Installment Loan B: five-year loan at 7.2% Use PMT= P n -nt to complete parts (a) through (c) below. a. Find the monthly payments and the total interest for Loan A. The monthly payment for Loan A is $. (Do not round until the final answer. Then round to the nearest cent as needed.) The total interest for Loan A is $. (Round to the nearest cent as needed.) b. Find the monthly payments and the total interest for Loan B. The monthly payment for Loan B is $.
Suppose that you decide to borrow $17,000 for a new car. You can select one of the following loans, each requiring regular monthly payments. Installment Loan A: three-year loan at 6.3% Installment Loan B: five-year loan at 7.2% Use PMT= P n -nt to complete parts (a) through (c) below. a. Find the monthly payments and the total interest for Loan A. The monthly payment for Loan A is $. (Do not round until the final answer. Then round to the nearest cent as needed.) The total interest for Loan A is $. (Round to the nearest cent as needed.) b. Find the monthly payments and the total interest for Loan B. The monthly payment for Loan B is $.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Car Loan Payment Calculation**
Suppose you decide to borrow $17,000 for a new car. You can select one of the following loans, each requiring regular monthly payments:
- **Installment Loan A**: Three-year loan at 6.3%
- **Installment Loan B**: Five-year loan at 7.2%
To calculate the monthly payments, use the formula:
\[
\text{PMT} = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-n \cdot t}}
\]
where:
- \( P \) is the principal loan amount ($17,000)
- \( r \) is the annual interest rate (0.063 for Loan A, 0.072 for Loan B)
- \( n \) is the number of payments per year (12 for monthly payments)
- \( t \) is the loan term in years (3 for Loan A, 5 for Loan B)
**Tasks:**
a. **Calculate the Monthly Payments and Total Interest for Loan A:**
- **Monthly Payment for Loan A**: Calculate using the formula above. Do not round until obtaining the final answer. Then, round to the nearest cent as needed.
- **Total Interest for Loan A**: Calculate the total amount paid over the term of the loan and subtract the principal to find the total interest paid. Round to the nearest cent as needed.
b. **Calculate the Monthly Payments and Total Interest for Loan B:**
- **Monthly Payment for Loan B**: Calculate using the formula above. Round to the nearest cent as needed.
- **Total Interest for Loan B**: Similarly, calculate the total amount paid over the loan term and subtract the principal. Round to the nearest cent as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8776e5e-a1de-48d6-ac3e-f9f0f44d4219%2F672e65ec-0e01-433c-9ed4-38bdede8993f%2Fcpbwhzl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Car Loan Payment Calculation**
Suppose you decide to borrow $17,000 for a new car. You can select one of the following loans, each requiring regular monthly payments:
- **Installment Loan A**: Three-year loan at 6.3%
- **Installment Loan B**: Five-year loan at 7.2%
To calculate the monthly payments, use the formula:
\[
\text{PMT} = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-n \cdot t}}
\]
where:
- \( P \) is the principal loan amount ($17,000)
- \( r \) is the annual interest rate (0.063 for Loan A, 0.072 for Loan B)
- \( n \) is the number of payments per year (12 for monthly payments)
- \( t \) is the loan term in years (3 for Loan A, 5 for Loan B)
**Tasks:**
a. **Calculate the Monthly Payments and Total Interest for Loan A:**
- **Monthly Payment for Loan A**: Calculate using the formula above. Do not round until obtaining the final answer. Then, round to the nearest cent as needed.
- **Total Interest for Loan A**: Calculate the total amount paid over the term of the loan and subtract the principal to find the total interest paid. Round to the nearest cent as needed.
b. **Calculate the Monthly Payments and Total Interest for Loan B:**
- **Monthly Payment for Loan B**: Calculate using the formula above. Round to the nearest cent as needed.
- **Total Interest for Loan B**: Similarly, calculate the total amount paid over the loan term and subtract the principal. Round to the nearest cent as needed.
Transcribed Image Text:Suppose that you decide to borrow $17,000 for a new car. You can select one of the following loans, each requiring:
(Round to the nearest cent as needed.)
b. Find the monthly payments and the total interest for Loan B.
- The monthly payment for Loan B is $____.
(Do not round until the final answer. Then round to the nearest cent as needed.)
- The total interest for Loan B is $____.
(Round to the nearest cent as needed.)
c. Compare the monthly payments and the total interest for the two loans.
Determine which loan is more economical. Choose the correct answer below.
- O A. The three-year loan at 6.3% is more economical.
- O B. The five-year loan at 7.2% is more economical.
The buyer will save approximately $____ in interest.
(Round to the nearest cent as needed.)
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