A mutual fund manager wishes to purchase a property that's 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, which is to be paid monthly. The annual interest rate on the loan is 2.45% and the loan is for 25 years. Calculate the total interest paid over the lifetime of the loan. 
Round your answer to the nearest hundred dollars.
Do NOT round until you have calculated the final answer.
 


Let's calculate the total interest paid over the lifetime of the loan step-by-step.

1. **Determine the loan amount:**

   The value of the property is $1,500,000, and the deposit is $200,000. The loan amount required is:

   \[
   \text{Loan Amount} = 1,500,000 - 200,000 = 1,300,000
   \]

2. **Calculate the monthly interest rate:**

   The annual interest rate is 2.45%, so the monthly interest rate is:

   \[
   \text{Monthly Interest Rate} = \frac{2.45}{12 \times 100} = 0.0020416667
   \]

3. **Calculate the number of monthly payments:**

   The loan is for 25 years, so the total number of monthly payments is:

   \[
   \text{Number of Payments} = 25 \times 12 = 300
   \]

4. **Calculate the monthly mortgage payment using the formula:**

   The formula for the monthly mortgage payment is:

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

   Where:
   - $ P $ is the loan amount ($1,300,000),
   - $ r $ is the monthly interest rate (0.0020416667),
   - $ n $ is the total number of payments (300).

   Plugging in the values:

   \[
   M = 1,300,000 \times \frac{0.0020416667 \times (1 + 0.0020416667)^{300}}{(1 + 0.0020416667)^{300} - 1}
   \]

   Let's compute this value.The monthly mortgage payment is approximately $5,799.34.

5. **Calculate the total amount paid over the lifetime of the loan:**

   \[
   \text{Total Payment} = \text{Monthly Payment} \times \text{Number of Payments}
   \]

   \[
   \text{Total Payment} = 5799.34 \times 300 = 1,739,800.10
   \]

6. **Calculate the total interest paid:**

   \[
   \text{Total Interest} = \text{Total Payment} - \text{Loan Amount}
   \]

   \[
   \text{Total Interest} = 1,739,800.10 - 1,300,000
   \]

Let's calculate the total interest paid over the lifetime of the loan.The total interest paid over the lifetime of the loan is approximately $439,800.

Would you like more details on any part of this calculation? Here are some related questions you might find useful:

1. How would the total interest change if the loan period were shorter, say 20 years?
2. What would be the effect of making an additional monthly payment towards the principal?
3. How much would the monthly payment be if the interest rate were 3% instead of 2.45%?
4. What is the total cost of the property after including the interest?
5. How is the amortization schedule structured for this loan?

**Tip:** Making extra payments towards the principal early in the loan can significantly reduce the total interest paid.

A mutual fund manager wishes to purchase a property that's 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, which is to be paid monthly. The annual interest rate on the loan is 2.45% and the loan is for 25 years. Calculate the total interest paid over the lifetime of the loan. Round your answer to the nearest hundred dollars. Do NOT round until you have calculated the final answer.

Learn how to calculate the total interest paid on a 25-year mortgage for a $1.5 million property at 2.45% interest. Detailed solution covers loan amortization, interest calculation, and the monthly mortgage payment formula. Suitable for college-level students or advanced high school learners.

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