Calculate the total interest paid over a mortgage of $260 000 amortized over 25 years at an annual interest rate of 6.49%. The mortgage payments are made on a monthly basis.

To calculate the total interest paid over the life of a mortgage, we need to determine the monthly mortgage payment and then use that to find the total amount paid over the term of the mortgage. Here is the step-by-step process:

1. **Determine the monthly mortgage payment using the formula:**

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

where:
- $ M $ is the monthly payment.
- $ P $ is the loan principal ($260,000).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the number of payments (loan term in years multiplied by 12).

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

\[ r = \frac{6.49\%}{12} = \frac{0.0649}{12} = 0.00540833 \]

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

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

4. **Plug these values into the mortgage payment formula:**

\[ M = 260,000 \times \frac{0.00540833(1+0.00540833)^{300}}{(1+0.00540833)^{300}-1} \]

Let's calculate this step by step.

First, calculate $(1 + r)^n$:

\[ (1 + 0.00540833)^{300} \approx 4.747561 \]

Next, calculate the numerator:

\[ 0.00540833 \times 4.747561 \approx 0.025673 \]

Then, calculate the denominator:

\[ 4.747561 - 1 = 3.747561 \]

Finally, calculate the monthly payment $ M $:

\[ M = 260,000 \times \frac{0.025673}{3.747561} \approx 260,000 \times 0.006852 \approx 1,781.63 \]

So, the monthly mortgage payment is approximately \$1,781.63.

5. **Calculate the total amount paid over the term of the mortgage:**

\[ \text{Total Amount Paid} = M \times n = 1,781.63 \times 300 = 534,489 \]

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

\[ \text{Total Interest Paid} = \text{Total Amount Paid} - \text{Principal} = 534,489 - 260,000 = 274,489 \]

Therefore, the total interest paid over the life of the mortgage is approximately \$274,489.

Would you like more details or have any questions about this calculation?

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**Related Questions:**

1. How does the interest rate affect the total interest paid over the life of the mortgage?
2. What would the monthly payment be if the interest rate were 5% instead of 6.49%?
3. How much would you save in total interest by reducing the mortgage term from 25 years to 20 years at the same interest rate?
4. What impact does making an additional monthly payment have on the total interest paid?
5. How would bi-weekly payments instead of monthly payments affect the mortgage?
6. What is the difference in total interest paid between a fixed-rate and an adjustable-rate mortgage?
7. How does refinancing the mortgage after 10 years affect the total interest paid?
8. What would be the total interest paid if the loan amount were $300,000 instead of $260,000?

**Tip:** Always compare different mortgage terms and interest rates to find the best option that minimizes total interest paid.

Learn how to calculate the total interest paid over a mortgage of $260,000 amortized over 25 years at an annual interest rate of 6.49%. This problem involves using the amortization formula to determine monthly payments and total interest paid. Suitable for adults looking to understand mortgage financing.

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