You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 30-year mortgage loan for 70 percent of the $3,300,000 purchase price. The monthly payment on this loan will be $16,300.

What is the APR on this loan?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

What is the EAR on this loan?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

### Step 1: Calculate the Loan Amount
First, we need to determine how much of the purchase price is being financed through the mortgage.

- **Purchase Price**: $3,300,000
- **Loan Percentage**: 70%

\[
\text{Loan Amount} = 70\% \times 3,300,000 = 0.70 \times 3,300,000 = 2,310,000
\]

So, the loan amount is **$2,310,000**.

### Step 2: Calculate the Monthly Interest Rate
We need to calculate the monthly interest rate using the given monthly payment, loan amount, and loan term. The loan term is 30 years, and the monthly payment is $16,300.

The monthly payment formula for a fixed-rate mortgage is:

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

Where:
- $ P $ is the monthly payment ($16,300),
- $ r $ is the monthly interest rate (what we're solving for),
- $ L $ is the loan amount ($2,310,000),
- $ n $ is the total number of payments (30 years × 12 months = 360 payments).

We can solve this equation numerically for $ r $, the monthly interest rate. Let me calculate that.The APR (Annual Percentage Rate) on the loan is **7.59%**.

### Step 3: Calculate the Effective Annual Rate (EAR)
The formula for the Effective Annual Rate (EAR) is:

\[
EAR = \left(1 + \frac{APR}{n}\right)^n - 1
\]

Where:
- $ APR $ is the annual percentage rate (7.59%),
- $ n $ is the number of compounding periods per year (12 for monthly payments).

Let me calculate the EAR now.It seems like I can’t do more advanced data analysis right now. Please try again later.

So far, we have determined that the APR on the loan is **7.59%**. If you'd like to continue with calculating the EAR or need further clarifications, feel free to ask.

Here are 5 related questions to deepen your understanding:
1. How does the APR differ from the nominal interest rate?
2. What impact does compounding frequency have on the EAR?
3. Can the APR change during the life of a mortgage loan?
4. How does the loan term affect the monthly mortgage payments?
5. What is the difference between a fixed-rate and an adjustable-rate mortgage?

**Tip**: When calculating the EAR, always remember that it takes into account the effects of compounding, unlike the APR.

You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 30-year mortgage loan for 70 percent of the $3,300,000 purchase price. The monthly payment on this loan will be $16,300. What is the APR on this loan? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. What is the EAR on this loan? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

Learn how to calculate the APR and EAR for a 30-year mortgage loan of $2,310,000 with a monthly payment of $16,300. This solution walks you through the loan payment formula and the effective annual rate calculation step by step. Ideal for finance students and professionals.

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