A hair stylist obtains a home loan for $414,000 at an annual interest rate of 5.75% compounded monthly for 30 years. Find the monthly mortgage payment (in dollars). round to the nearest cent 

To calculate the monthly mortgage payment for a loan, we use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ is the monthly payment
- $P$ is the loan principal (initial amount), which is $414,000$
- $r$ is the monthly interest rate, calculated as the annual interest rate divided by 12. The annual interest rate is $5.75\%$, so $r = \frac{5.75\%}{12} = \frac{0.0575}{12} = 0.00479167$
- $n$ is the total number of payments (number of months), which is $30 \times 12 = 360$ months for a 30-year mortgage

Let’s now calculate the monthly payment $M$.The monthly mortgage payment is approximately **$2,415.99**.

Would you like more details or have any further questions? 

Here are 5 related questions:
1. How would the payment change if the interest rate was reduced to 4.5%?
2. What is the total amount paid over the 30 years?
3. How much interest is paid over the life of the loan?
4. What would happen if the loan term was shortened to 20 years?
5. How does the compounding frequency affect the total payment?

**Tip:** Making extra payments towards the principal can reduce the overall interest paid and shorten the loan term!

A hair stylist obtains a home loan for $414,000 at an annual interest rate of 5.75% compounded monthly for 30 years. Find the monthly mortgage payment (in dollars). Round to the nearest cent.

Calculate the monthly mortgage payment for a $414,000 home loan with a 5.75% interest rate, compounded monthly for 30 years. This guide provides a detailed step-by-step solution using the loan amortization formula. Ideal for students in Grades 10-12.

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