You have just purchased a new warehouse. To finance the purchase, you’ve arranged a 25-year mortgage for 85 percent of the $2,400,000 purchase price. The monthly payment on this loan will be $16,500. What is the APR on this loan? 

To calculate the APR (Annual Percentage Rate) on this mortgage loan, we need to apply the formula for the monthly payment of a fixed-rate mortgage. The formula for the monthly payment $ M $ is:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan principal (the amount borrowed).
- $ r $ is the monthly interest rate (APR divided by 12).
- $ n $ is the total number of payments (loan term in months).

### Step 1: Determine the loan principal and loan term
- Purchase price = $2,400,000
- Loan is for 85% of the purchase price: 
  \[
  P = 0.85 \times 2,400,000 = 2,040,000
  \]
- Loan term = 25 years = 25 × 12 = 300 months.
- Monthly payment $ M = 16,500 $.

### Step 2: Rearranging the formula to solve for $ r $
Since the formula involves both $ r $ and its powers, it's a complex equation that cannot be solved algebraically by simple manipulation. Instead, we use numerical methods to solve for $ r $.

Let me calculate the monthly interest rate $ r $, then convert it to an APR.The APR (Annual Percentage Rate) on this loan is approximately **8.55%**.

Would you like a more detailed breakdown of the steps or any other explanation?

Here are some related questions for further exploration:
1. What factors affect the APR on a mortgage?
2. How would increasing the down payment affect the APR and monthly payments?
3. What is the difference between APR and the nominal interest rate?
4. How does the loan term influence the total interest paid over the life of a loan?
5. How would an early payment plan affect the overall interest paid?

**Tip:** The APR includes both the interest rate and any associated fees or costs related to the loan, giving a more comprehensive picture of the loan's cost.

You have just purchased a new warehouse. To finance the purchase, you’ve arranged a 25-year mortgage for 85 percent of the $2,400,000 purchase price. The monthly payment on this loan will be $16,500. What is the APR on this loan?

Learn how to calculate the APR on a 25-year mortgage for a warehouse purchase. This example involves a loan of $2,040,000 (85% of the $2,400,000 purchase price) with a monthly payment of $16,500. The solution uses mortgage formulas and numerical methods to find the APR, which is approximately 8.55%.

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