An orthodontist obtains a 30-year home loan for $595,000 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 calculate the monthly mortgage payment for a loan, we use the formula for a fixed-rate mortgage:

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

Where:
- $M$ = monthly mortgage payment
- $P$ = loan principal (\$595,000)
- $r$ = monthly interest rate (annual rate divided by 12)
- $n$ = total number of payments (number of years × 12)

### Step-by-step:

1. **Loan principal ($P$)**: \$595,000
2. **Annual interest rate**: 4.175%
    - Monthly interest rate: $ r = \frac{4.175\%}{12} = \frac{0.04175}{12} = 0.003479167 $
3. **Number of payments ($n$)**: 30 years × 12 months/year = 360 payments

Now plug these values into the formula:

\[
M = 595,000 \times \frac{0.003479167(1+0.003479167)^{360}}{(1+0.003479167)^{360} - 1}
\]

I'll calculate this.The monthly mortgage payment is approximately **$2,900.98**.

Would you like more details or have any questions about the calculation? Here are five related questions to expand on this concept:

1. How does the mortgage payment change if the interest rate increases by 1%?
2. What is the total amount paid over the life of the loan?
3. How much of the first payment goes towards interest versus principal?
4. What is the balance of the loan after 10 years of payments?
5. How does the loan term affect the monthly payment?

**Tip:** Small changes in the interest rate can have a significant impact on monthly mortgage payments, especially over long loan terms.

An orthodontist obtains a 30-year home loan for $595,000 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 loan of $595,000 with a 4.175% interest rate, compounded monthly. This step-by-step guide covers financial mathematics concepts, including the fixed-rate mortgage formula, suitable for advanced high school students or undergraduates.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation