Suppose you borrow $447,000 for a home loan.

The interest rate is 11% per annum nominal, and the loan is for 20 years.

If you make monthly repayments, how much is each repayment?


To calculate the monthly repayment on the home loan, we will use the **amortization formula**, which calculates the fixed monthly payment needed to pay off a loan over a specific time period.

The formula for the monthly payment $ M $ is:

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

Where:
- $ P $ is the loan amount (principal),
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments (months),
- $ M $ is the monthly payment.

### Given:
- Loan amount $ P = 447,000 $
- Annual nominal interest rate = 11%, so monthly interest rate $ r = \frac{11\%}{12} = \frac{0.11}{12} $
- Loan term = 20 years, so total number of payments $ n = 20 \times 12 = 240 $ months.

Let's calculate the monthly repayment.# Variables for the calculation
P = 447000  # Principal loan amount
annual_interest_rate = 0.11  # 11% annual nominal interest rate
n = 20 * 12  # 20 years * 12 months per year = 240 total payments

# Monthly interest rate
r = annual_interest_rate / 12  # Convert annual interest rate to monthly

# Amortization formula: M = P * [r(1 + r)^n] / [(1 + r)^n - 1]
M = P * (r * (1 + r) ** n) / ((1 + r) ** n - 1)
MThe monthly repayment on the home loan would be approximately **$4,613.88**.

Let me know if you have any questions or would like further explanation!

Here are 5 related questions:
1. How would your monthly repayment change if the interest rate were reduced by 1%?
2. What would be the total interest paid over the life of the loan?
3. How does increasing the loan term to 30 years affect the monthly repayment?
4. What impact does making an extra monthly payment have on the total loan term?
5. How would switching from monthly to bi-weekly payments influence the loan payoff timeline?

**Tip:** Extra payments on your loan, even small ones, can significantly reduce the total interest paid and shorten the loan term.

Learn how to calculate the monthly repayment for a $447,000 home loan with an 11% annual interest rate over 20 years. Use the amortization formula to find the fixed monthly payment. Discover how adjustments in interest rates and loan terms affect repayments.

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