Find the required monthly payment for a 30-year home mortgage in the amount of $200,000 with an APR of 5.00%, compounded monthly.



 $1,313


 $1,074


 $1,045


 $1,251


 None of the above.

To find the required monthly payment for a 30-year mortgage, we can use the following formula for a fixed-rate mortgage:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount (principal).
- $ 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 for monthly payments).

### Given:
- $ P = 200,000 $
- Annual interest rate $ = 5\% $
- Monthly interest rate $ r = \frac{5\%}{12} = \frac{0.05}{12} = 0.004167 $
- Loan term $ = 30 $ years, so total number of payments $ n = 30 \times 12 = 360 $

Now, plugging the values into the formula:

\[
M = 200,000 \frac{0.004167(1 + 0.004167)^{360}}{(1 + 0.004167)^{360} - 1}
\]

Let's calculate this.The required monthly payment for the 30-year mortgage is approximately **$1,073.64**. Therefore, the correct answer is **$1,074**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How does the term length affect monthly mortgage payments?
2. What is the difference between APR and nominal interest rates?
3. How do extra payments affect a mortgage's total interest paid?
4. What happens if the APR changes in an adjustable-rate mortgage?
5. How would the monthly payment change if the loan amount was $300,000?

**Tip:** Making biweekly mortgage payments can reduce the loan term and total interest paid.

Find the required monthly payment for a 30-year home mortgage in the amount of $200,000 with an APR of 5.00%, compounded monthly.

Learn how to calculate the monthly payment for a $200,000 mortgage with an APR of 5% over 30 years, using the loan amortization formula. This problem demonstrates interest rate calculations and loan amortization, making it suitable for advanced high school or college students.

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