You can afford a $450 per month car payment. You've found a 5 year loan at 7% interest. How big of a loan can you afford?
You can afford a $450 per month car payment. You've found a 5 year loan at 7% interest. How big of a loan can you afford?
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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![The text on the image reads:
"You can afford a $450 per month car payment. You've found a 5-year loan at 7% interest. How big of a loan can you afford?"
There is a blank box with a dollar symbol ($) indicating where the answer should be inputted.
To calculate the loan amount you can afford, you can use the formula for calculating the present value of an annuity:
\[ P = \frac{PMT \times (1 - (1 + r)^{-n})}{r} \]
Where:
- \( P \) is the loan amount (present value).
- \( PMT \) is the monthly payment ($450).
- \( r \) is the monthly interest rate (7% annual interest rate divided by 12 months, or approximately 0.005833).
- \( n \) is the total number of payments (5 years × 12 months = 60).
Plug the numbers into the formula to compute the loan amount you can afford.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40759b05-e7b6-4224-af99-62d06fa9c7b0%2Fe251d84b-8988-445d-bd7a-2ccdc8b48b17%2F3x1agtnl_processed.png&w=3840&q=75)
Transcribed Image Text:The text on the image reads:
"You can afford a $450 per month car payment. You've found a 5-year loan at 7% interest. How big of a loan can you afford?"
There is a blank box with a dollar symbol ($) indicating where the answer should be inputted.
To calculate the loan amount you can afford, you can use the formula for calculating the present value of an annuity:
\[ P = \frac{PMT \times (1 - (1 + r)^{-n})}{r} \]
Where:
- \( P \) is the loan amount (present value).
- \( PMT \) is the monthly payment ($450).
- \( r \) is the monthly interest rate (7% annual interest rate divided by 12 months, or approximately 0.005833).
- \( n \) is the total number of payments (5 years × 12 months = 60).
Plug the numbers into the formula to compute the loan amount you can afford.
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