An orthodontist obtains a 30-year home loan for $515,000 at an annual interest rate of 4.175% compounded monthly. Find the monthly mortgage payment (in dollars). (Round your answer to the nearest cent.)

To find the monthly mortgage payment, we use the formula for the monthly payment of a fixed-rate mortgage:

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

Where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the principal loan amount (in this case, $ 515,000 $).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (loan term in years multiplied by 12 months per year).

### Step-by-step:
1. Principal $ P = 515,000 $
2. Annual interest rate = 4.175%, so monthly interest rate $ r = \frac{4.175}{100} \div 12 = 0.00347917 $
3. Loan term = 30 years, so total number of payments $ n = 30 \times 12 = 360 $

Now, let's calculate the monthly mortgage payment:

\[
M = \frac{515,000 \cdot 0.00347917 \cdot (1 + 0.00347917)^{360}}{(1 + 0.00347917)^{360} - 1}
\]

I'll compute this.The monthly mortgage payment is approximately **$2,510.93**.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How would the monthly payment change if the interest rate increased to 5%?
2. What is the total interest paid over the life of the loan?
3. How much would be saved by paying off the loan 5 years early?
4. How does compounding monthly affect the total amount paid compared to annual compounding?
5. What happens if extra payments are made towards the principal?

**Tip:** Making extra payments towards the principal can significantly reduce the total interest paid over the life of the loan.

An orthodontist obtains a 30-year home loan for $515,000 at an annual interest rate of 4.175% compounded monthly. Find the monthly mortgage payment (in dollars). (Round your answer to the nearest cent.)

Learn how to calculate the monthly mortgage payment for a 30-year home loan of $515,000 with an interest rate of 4.175% compounded monthly. This financial math problem uses the fixed-rate mortgage formula and explores key concepts in loan amortization and compound interest. Suitable for college-level students or those studying financial math.

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