Decreasing the number of years of a loan decreases the amount of interest repaid over the term of the loan. Suppose a dental hygienist has the option of a 30-year loan or a 25-year loan of $365,000 at an annual interest rate of 5.25%.

(a)

Calculate the monthly payment (in dollars) for each loan. (Round your answers to the nearest cent.)

To calculate the monthly payment for a loan, we can use the standard formula for a fixed-rate mortgage or loan, which is given by:

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

Where:
- $M$ is the monthly payment.
- $P$ is the loan amount.
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of monthly payments (loan term in years multiplied by 12).

Given:
- Loan amount $P = 365,000$
- Annual interest rate = 5.25% = 0.0525
- For the 30-year loan, $n = 30 \times 12 = 360$ months.
- For the 25-year loan, $n = 25 \times 12 = 300$ months.

Let's first calculate the monthly payment for both the 30-year loan and the 25-year loan. I will compute these values.The monthly payments for each loan are as follows:

- For the 30-year loan: **$2015.54**
- For the 25-year loan: **$2187.25**

Would you like further details or have any questions?

Here are five related questions:
1. How does reducing the loan term affect total interest paid?
2. What would happen if the interest rate changed?
3. How does the down payment influence monthly payments?
4. What are the benefits of a shorter loan term, besides saving on interest?
5. How do property taxes and insurance affect monthly payments?

**Tip:** Making extra payments on a loan, even occasionally, can significantly reduce the overall interest paid over time.

Decreasing the number of years of a loan decreases the amount of interest repaid over the term of the loan. Suppose a dental hygienist has the option of a 30-year loan or a 25-year loan of $365,000 at an annual interest rate of 5.25%. (a) Calculate the monthly payment (in dollars) for each loan. (Round your answers to the nearest cent.)

Learn how to calculate monthly payments for a $365,000 loan with options of 30-year and 25-year terms at an annual interest rate of 5.25%. Using the loan amortization formula, find out the monthly payments for both loan terms and understand how loan duration impacts total interest paid.

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