To calculate the remaining loan balance after 6 years, we will use the amortization formula for a loan, which is given by:

$B = P \times \frac{(1 + r)^n - (1 + r)^p}{(1 + r)^n - 1}$

Where:

• $B$ is the remaining loan balance.
• $P$ is the loan amount (principal).
• $r$ is the monthly interest rate (annual rate divided by 12).
• $n$ is the total number of payments (loan amortization period in months).
• $p$ is the number of payments made after 6 years (payments per year times 6).

Step 1: Identify the loan amount

The loan-to-value ratio (LTV) is 60%, meaning the loan covers 60% of the building's purchase price.

$P = 60\% \times 5,000,000 = 0.60 \times 5,000,000 = 3,000,000$

Step 2: Monthly interest rate

The annual interest rate is 5.25%, so the monthly interest rate $r$ is:

$r = \frac{5.25\%}{12} = \frac{0.0525}{12} = 0.004375$

Step 3: Number of payments

The loan is amortized over 25 years, so the total number of payments $n$ is:

$n = 25 \times 12 = 300 \text{ payments}$

Step 4: Payments made after 6 years

After 6 years, the number of payments $p$ made is:

$p = 6 \times 12 = 72 \text{ payments}$

Step 5: Calculate remaining loan balance

Now, we can calculate the remaining loan balance $B$. I will calculate this for you.The remaining loan balance at the end of 6 years would be approximately $2,590,379.16.

Would you like further details on how this calculation works or have any other questions?

Here are 5 related questions to expand on this information:

1. How would the remaining loan balance change if the interest rate were lower?
2. What impact does making additional principal payments have on the remaining balance?
3. How can we calculate the total interest paid over the 6 years?
4. What is the effect of a shorter loan amortization period on monthly payments and the remaining balance?
5. How does the loan-to-value ratio affect the initial loan amount?

Tip: Making extra payments toward your principal can significantly reduce the overall interest paid on a loan.