A mutual fund manager wishes to purchase a property that's been valued at  
$
1.5
  m. She has  
$
200
,
000
  in cash to use as a deposit, and she will require a mortgage for the rest. The annual interest rate on the loan is  
2.45
%
  and the loan is for  
25
  years. Calculate the monthly repayments. Give your answer in dollars and cents. Do not include commas or the dollar sign in your answer.

To calculate the monthly repayments for the loan, we use the following formula for a fixed-rate mortgage:

\[
M = P \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Where:
- $M$ is the monthly repayment.
- $P$ is the principal loan amount.
- $r$ is the monthly interest rate.
- $n$ is the number of monthly payments (loan term in months).

### Step 1: Calculate the principal loan amount $P$.
The property is valued at \$1.5 million, and the buyer has \$200,000 for a deposit. The loan amount is:

\[
P = 1,500,000 - 200,000 = 1,300,000
\]

### Step 2: Convert the annual interest rate to a monthly interest rate.
The annual interest rate is 2.45%, so the monthly interest rate is:

\[
r = \frac{2.45}{100 \times 12} = 0.00204167
\]

### Step 3: Calculate the total number of monthly payments.
The loan term is 25 years, so the total number of monthly payments is:

\[
n = 25 \times 12 = 300
\]

### Step 4: Apply the mortgage formula.
Now we can calculate the monthly repayment:

\[
M = 1,300,000 \times \frac{0.00204167 \times (1 + 0.00204167)^{300}}{(1 + 0.00204167)^{300} - 1}
\]

Let me calculate that for you.The monthly repayment is approximately **5799.34** dollars.

Would you like more details or have any questions?

Here are five related questions:
1. How does an increase in the interest rate affect monthly repayments?
2. What would the monthly repayment be if the loan term was 30 years instead of 25?
3. How is the total amount of interest paid over the loan term calculated?
4. What happens if the borrower makes an additional payment each month?
5. How does a down payment affect the mortgage loan amount?

**Tip:** A longer loan term reduces monthly payments but increases the total interest paid.

A mutual fund manager wishes to purchase a property that's been valued at $1.5 million. She has $200,000 in cash to use as a deposit, and she will require a mortgage for the rest. The annual interest rate on the loan is 2.45% and the loan is for 25 years. Calculate the monthly repayments. Give your answer in dollars and cents. Do not include commas or the dollar sign in your answer.

Learn how to calculate the monthly repayments on a $1.3 million mortgage loan with a 2.45% annual interest rate and a 25-year loan term. This detailed solution uses the fixed-rate mortgage formula and explains the key concepts of loan repayment and interest rates. Suitable for high school students in Grades 11-12.

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