You are applying for a loan to purchase a shopping center. You can afford no more than $15,000, monthly (PMT). The lender informs you that interest rates are at 4% (RATE) and typical loan amortization periods are 25 years (NPER). What is the most you can borrow (PV)? 

To determine the most you can borrow (PV), we can use the **Present Value of an Annuity** formula:

\[
PV = \frac{PMT \times \left(1 - (1 + RATE)^{-NPER}\right)}{RATE}
\]

Where:
- $ PMT $ is the monthly payment ($15,000)
- $ RATE $ is the monthly interest rate (annual rate of 4% divided by 12 months)
- $ NPER $ is the number of periods (25 years multiplied by 12 months per year)

First, let's calculate the values:

1. $ PMT = 15,000 $
2. $ RATE = \frac{4\%}{12} = 0.04 / 12 = 0.003333 $
3. $ NPER = 25 \times 12 = 300 $ months

Now we can calculate $ PV $.

I'll solve it for you.The most you can borrow (PV) is approximately **$2,841,787.24**.

Would you like more details on the calculation, or do you have any questions?

Here are some related questions you might consider:
1. How does the loan amount change if the interest rate increases to 5%?
2. What would happen if the loan period changes from 25 to 30 years?
3. How would the monthly payment change if you borrow $3,000,000 instead?
4. What is the total interest paid over the life of the loan?
5. How does changing the payment frequency (e.g., bi-weekly) affect the total loan cost?

**Tip:** The longer the amortization period, the lower your monthly payments, but the more interest you will pay overall.

You are applying for a loan to purchase a shopping center. You can afford no more than $15,000, monthly (PMT). The lender informs you that interest rates are at 4% (RATE) and typical loan amortization periods are 25 years (NPER). What is the most you can borrow (PV)?

Learn how to calculate the maximum loan you can borrow for purchasing a shopping center with a monthly payment of $15,000, a 4% interest rate, and a 25-year amortization period. This problem covers key financial concepts like loan amortization, present value, and annuities. Suitable for advanced high school and college-level students.

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