Suppose you want to borrow ​$100 comma 000 and you find a bank offering a 40​-year term for a loan of that​ amount, with an APR of 6​%. Complete parts ​(a) and ​(b) below.
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Part 1
​(a) What are your monthly​ payments?
PMTequals​$
  
enter your response here
​(Round to the nearest cent as​ needed.

To calculate the monthly payments (PMT) for a loan, we use the formula for the monthly payment on an amortizing loan:

\[
PMT = \frac{P \times r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $P$ is the loan amount ($100,000),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the total number of payments (number of years multiplied by 12).

Given:
- $P = 100,000$
- Annual interest rate = 6%, so monthly interest rate $r = \frac{6\%}{12} = 0.005$
- Loan term = 40 years, so $n = 40 \times 12 = 480$ months.

Now, let's calculate the monthly payment.

The monthly payment (PMT) for a loan of $100,000 at an APR of 6% over 40 years is approximately **$550.21**.

Would you like further details or have any questions? Here are some related questions to explore:

1. How does the loan term affect monthly payments?
2. What is the total interest paid over the life of this loan?
3. How do different APR rates impact the monthly payment?
4. How would a shorter loan term (e.g., 30 years) change the monthly payment?
5. What if you make additional payments—how does that affect the overall cost?

**Tip**: The longer the loan term, the lower the monthly payments, but more interest accumulates over time.

Suppose you want to borrow ​$100,000 and you find a bank offering a 40​-year term for a loan of that​ amount, with an APR of 6​%. Complete parts ​(a) and ​(b) below. (a) What are your monthly​ payments? (PMT) (Round to the nearest cent as​ needed.)

Learn how to calculate the monthly payments for a $100,000 loan at an APR of 6% over a 40-year term. This problem uses the loan amortization formula to find the payment amount and covers concepts related to interest rates and monthly payments.

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