To answer your questions, we'll go step by step through each of the parts.

Part 1: Monthly Payment on the Loan

1. The investor plans to buy a property worth $2 million with 5% down payment and an annual interest rate of 5% for 12 years.

   • Loan Amount:
     Since the investor is paying 5% down, they are borrowing 95% of the property value.
     $\text{Loan Amount} = 2,000,000 \times (1 - 0.05) = 1,900,000$

   • Interest Rate:
     The annual interest rate is 5%, so the monthly interest rate is: $\text{Monthly Interest Rate} = \frac{5}{12} = 0.41667\% = 0.004167$

   • Loan Term:
     The loan term is 12 years, so in months, it's: $\text{Term in Months} = 12 \times 12 = 144 \text{ months}$

Now, we calculate the monthly payment using the standard formula for a fixed-rate mortgage:

$M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}$ Where:

• $M$ = monthly payment
• $P$ = loan amount = 1,900,000
• $r$ = monthly interest rate = 0.004167
• $n$ = number of months = 144

Let’s compute this now.

Part 2: Monthly Growth Rate of Property Value Over 4 Years

The property will be sold for $2.25 million after 4 years. To determine the monthly growth rate, we use the formula for compound growth:

$FV = PV(1 + r)^n$

Where:

• $FV$ = future value = 2.25 million
• $PV$ = present value = 2 million
• $r$ = monthly growth rate
• $n$ = number of months = 4 years × 12 = 48 months

We solve for $r$ using the equation:

$\left(\frac{FV}{PV}\right) = (1 + r)^n$ $\frac{2.25}{2} = (1 + r)^{48}$

Let’s compute the monthly growth rate $r$.

Part 3: Return on Selling the Property After Four Years

The return from selling the property is calculated as the profit made on the sale, expressed as a percentage of the initial investment.

$\text{Return} = \frac{\text{Sale Price} - \text{Initial Investment}}{\text{Initial Investment}} \times 100$

Here:

• Sale price = $2.25 million
• Initial investment = 5% down payment on $2 million = $100,000

We can now compute the return on the investment.

Let's calculate these values.### Part 1: Monthly Payment on the Loan The monthly payment on the loan is approximately $17,572.92.

Part 2: Monthly Growth Rate of the Property

The monthly growth rate for the value of the property over 4 years is approximately 0.25%.

Part 3: Return from Selling the Property After Four Years

The return from selling the property after four years, based on the initial down payment, is 2150%.

This return is calculated as a percentage of the initial investment of $100,000 (5% of $2 million). The high return is due to leveraging (only a small down payment) and the increase in the property's value.

---

Would you like more details or have any further questions? Here are a few related questions:

1. How would the monthly payment change if the interest rate increased to 6%?
2. What would be the total interest paid over the life of the loan?
3. How would the return change if the property sold for $2.5 million instead?
4. What if the investor chose a shorter loan term of 10 years instead of 12 years?
5. How much equity would the investor build after four years if they continued paying the mortgage?

Tip: Leverage can significantly amplify returns on investments but also increases risk, especially if property values decrease.