You are applying for a loan to purchase a shopping center. You can afford no more than $25,000, monthly (PMT). The lender informs you that interest rates are at 6.25% (RATE) and typical loan amortization periods are 20 years (NPER). What is the most you can borrow (PV)? 

To find the maximum loan amount (Present Value, PV) that you can borrow, we can use the formula for the Present Value of an annuity, which is:

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

However, since the payments are monthly, we need to adjust the interest rate and the number of periods to reflect monthly compounding. Here are the adjustments:

- Monthly interest rate = Annual interest rate / 12 = 6.25% / 12 = 0.0052083
- Total number of monthly periods = Years × 12 = 20 × 12 = 240 months

Thus, we will use the formula:

\[
PV = PMT \times \left( \frac{1 - (1 + \frac{RATE}{12})^{-240}}{\frac{RATE}{12}} \right)
\]

Let's compute the maximum loan amount.The maximum loan amount you can borrow, given your monthly payment limit of $25,000, an interest rate of 6.25%, and a 20-year amortization period, is approximately **$3,420,308.58**.

Do you have any questions, or would you like more details on the calculations?

Here are 5 related questions to further explore:
1. How would changes in interest rates affect the maximum loan amount?
2. What happens if the loan period is extended to 25 or 30 years?
3. What would your monthly payment be if you borrowed $4 million under the same terms?
4. How does the down payment factor into the total cost of the loan?
5. What is the difference between fixed-rate and variable-rate loans?

**Tip:** When shopping for loans, always compare the total interest cost over the life of the loan, not just the monthly payments.

You are applying for a loan to purchase a shopping center. You can afford no more than $25,000, monthly (PMT). The lender informs you that interest rates are at 6.25% (RATE) and typical loan amortization periods are 20 years (NPER). What is the most you can borrow (PV)?

Learn how to calculate the maximum loan amount you can borrow with a monthly payment of $25,000, an interest rate of 6.25%, and a 20-year loan term. This finance problem covers the Present Value of Annuity formula, making it ideal for college-level finance or business students.

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