You are applying for a loan to purchase a shopping center. You can afford no more than $23,425, monthly (PMT). The lender informs you that interest rates are at 6.75% (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 **loan amortization formula**, which is derived from the formula for the present value of an annuity:

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

Where:
- $ PMT = 23,425 $ (monthly payment),
- $ RATE = \frac{6.75\%}{12} = \frac{0.0675}{12} $ (monthly interest rate),
- $ NPER = 25 \times 12 = 300 $ months (total number of payments).

Let me calculate that for you.The most you can borrow (PV) is approximately **$3,390,448.58**.

Would you like a detailed breakdown of how the formula works, or do you have any questions?

Here are 5 related questions you might explore:
1. What would happen if the interest rate increased to 7%?
2. How does the loan amount change with a shorter loan period (e.g., 20 years)?
3. What if the monthly payment was increased to $25,000?
4. How does changing the down payment affect the amount you can borrow?
5. What is the total amount of interest paid over the life of the loan?

**Tip:** Small changes in the interest rate can have a significant effect on the loan amount due to the long-term compounding effects of interest.

You are applying for a loan to purchase a shopping center. You can afford no more than $23,425, monthly (PMT). The lender informs you that interest rates are at 6.75% (RATE) and typical loan amortization periods are 25 years (NPER). What is the most you can borrow (PV)?

Learn how to calculate the maximum amount you can borrow when purchasing a shopping center, based on a 6.75% interest rate and a monthly payment of $23,425. This detailed solution uses the present value of annuities formula, covering concepts like interest rates, loan amortization, and payment terms. Suitable for advanced high school students and finance majors.

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