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, 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.

To calculate the total interest paid over the lifetime of the loan, we'll follow these steps:

1. **Determine the loan amount (principal):**

   The property value is $1,500,000, and the deposit is $200,000. The loan amount (principal) is:
   \[
   \text{Principal} = \$1,500,000 - \$200,000 = \$1,300,000
   \]

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

   The annual interest rate is 2.45%. To find the monthly interest rate, divide the annual rate by 12:
   \[
   \text{Monthly Interest Rate} = \frac{2.45\%}{12} = \frac{0.0245}{12} = 0.00204167
   \]

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

   The loan term is 25 years. Convert this to months:
   \[
   \text{Number of Payments} = 25 \times 12 = 300
   \]

4. **Calculate the monthly mortgage payment using the formula for an amortizing loan:**

   The formula for the monthly mortgage payment $ M $ is:
   \[
   M = P \times \frac{r(1+r)^n}{(1+r)^n-1}
   \]
   Where:
   - $ P $ is the principal amount ($1,300,000)
   - $ r $ is the monthly interest rate (0.00204167)
   - $ n $ is the number of payments (300)

   Plugging in the values:
   \[
   M = 1{,}300{,}000 \times \frac{0.00204167(1 + 0.00204167)^{300}}{(1 + 0.00204167)^{300} - 1}
   \]

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

   Once we have $ M $, the total amount paid over 25 years is:
   \[
   \text{Total Amount Paid} = M \times 300
   \]

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

   The total interest paid is the total amount paid minus the principal:
   \[
   \text{Total Interest Paid} = \text{Total Amount Paid} - P
   \]

Now, let's calculate these values.

\[
M = 1{,}300{,}000 \times \frac{0.00204167 \times (1.00204167)^{300}}{(1.00204167)^{300} - 1}
\]
\[
M \approx 1{,}300{,}000 \times \frac{0.00204167 \times 2.077057}{2.077057 - 1} 
\]
\[
M \approx 1{,}300{,}000 \times \frac{0.00423916}{1.077057} 
\]
\[
M \approx 1{,}300{,}000 \times 0.00393477 \approx 5{,}115.20
\]

**Total Amount Paid**:
\[
\text{Total Amount Paid} = 5{,}115.20 \times 300 = 1{,}534{,}560
\]

**Total Interest Paid**:
\[
\text{Total Interest Paid} = 1{,}534{,}560 - 1{,}300{,}000 \approx 234{,}560
\]

Rounding to the nearest hundred dollars:

\[
\text{Total Interest Paid} \approx 234{,}600
\]

Thus, the total interest paid over the lifetime of the loan is approximately **$234,600**.

Do you want more details or have any questions?

Here are 5 related questions:

1. How does the length of the loan term affect the total interest paid?
2. What would be the impact of a higher interest rate on the total interest paid?
3. How much would the monthly payment change if the loan term were reduced to 20 years?
4. What is the effect of increasing the down payment on the total interest paid?
5. How does paying extra toward the principal each month affect the total interest paid?

**Tip:** Making additional payments toward your principal can significantly reduce the total interest paid over the life of the loan.

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, 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 $1.5 million mortgage with a 2.45% annual interest rate over 25 years. This problem involves key concepts in loan amortization and interest calculation. Suitable for students in Grades 11-12.

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