What is the APR of a 30-year, $300,000 mortgage with monthly payments of $ 2250?

To calculate the **Annual Percentage Rate (APR)** of a mortgage, we can use the formula for the monthly mortgage payment:

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

Where:
- $M$ is the monthly payment (\$2,250),
- $P$ is the loan principal (\$300,000),
- $r$ is the monthly interest rate (which we want to find),
- $n$ is the total number of payments (30 years × 12 months = 360 payments).

We can rearrange the equation to solve for $r$ using numerical methods, then multiply the monthly interest rate by 12 to convert it to the annual percentage rate (APR).

Let's solve for $r$.The Annual Percentage Rate (APR) for the 30-year, \$300,000 mortgage with monthly payments of \$2,250 is approximately **8.23%**.

Would you like more details on how this was calculated or any clarification? 

Here are 5 related questions to explore further:
1. How does the APR differ from the nominal interest rate?
2. What would the monthly payment be with a lower APR, say 7%?
3. How much total interest would be paid over the life of the loan?
4. What effect does making extra monthly payments have on the total interest paid?
5. How does the loan term (e.g., 15 years vs. 30 years) impact the APR?

**Tip**: Lowering the interest rate by even a small amount can save you thousands over the life of a mortgage.

What is the APR of a 30-year, $300,000 mortgage with monthly payments of $2250?

Learn how to calculate the APR for a 30-year, $300,000 mortgage with monthly payments of $2250. This guide uses the loan amortization formula to determine the monthly interest rate and convert it to an annual percentage rate (APR). Suitable for finance students and home buyers.

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