What would be the sum of all the payments made on the following house mortgage? Loan amount is $247,000 with an interest rate of 7.9% per annum, term of 30 years, and monthly payments.

To calculate the total sum of all payments made on the house mortgage, we first need to determine the monthly payment using the formula for a fixed-rate mortgage:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount (principal), which is $247,000.
- $ r $ is the monthly interest rate, which is the annual interest rate divided by 12. For an interest rate of 7.9% per annum, $ r = \frac{7.9\%}{12} = \frac{0.079}{12} $.
- $ n $ is the total number of payments, which is the number of years multiplied by 12. For a 30-year term, $ n = 30 \times 12 = 360 $ months.

Let's calculate the monthly payment and then the total sum of all payments.The monthly payment on the mortgage would be approximately **$1,795.21**.

The total sum of all payments made over the 30-year term would be approximately **$646,275.37**.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What is the total interest paid over the life of the loan?
2. How does increasing the term to 40 years affect the total payments?
3. What happens if the interest rate drops to 5% instead?
4. How much would the monthly payment be with a 15-year term?
5. What is the principal balance after 10 years of payments?

**Tip:** Paying extra towards the principal each month can significantly reduce the total interest paid over the life of the loan.

Discover how to calculate the total payments for a $247,000 mortgage with a 7.9% interest rate over 30 years. This example covers key concepts in loan amortization, including monthly payment calculations using the fixed-rate mortgage formula. Ideal for students in Grades 11-12.

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