A Sydney couple had considered buying a house back in 2020 when home loans could have been had at an APR of 2.5% (assume monthly compounding throughout). Unfortunately, they did not have the necessary down payment at the time. Now, they finally have saved up the down payment, but home loans more likely come with an interest rate of 6.4% now. Assume a loan amount of A$1.8 million and an amortization period of 25 years at both points in time.
What would have been the monthly loan repayment in 2020?

To determine the monthly loan repayment, we will use the formula for calculating the monthly payment for a fixed-rate mortgage, which is based on the **loan amount**, **interest rate**, and the **amortization period**:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount (A\$1.8 million).
- $ r $ is the monthly interest rate (annual percentage rate divided by 12).
- $ n $ is the total number of payments (years of amortization multiplied by 12 months per year).

### Step 1: Plug in the values for 2020 (APR = 2.5%)
- $ P = 1,800,000 \, \text{AUD} $
- Annual interest rate = 2.5% → Monthly interest rate = $\frac{2.5\%}{12} = \frac{0.025}{12} \approx 0.002083 $
- Amortization period = 25 years → $ n = 25 \times 12 = 300 $ months

Let's calculate the monthly payment for the 2020 scenario.The monthly loan repayment in 2020, when the interest rate was 2.5%, would have been approximately **A$8,075.10**.

Would you like further details or have any questions about this calculation? Here are five related questions to explore:

1. How does the monthly repayment change with the current interest rate of 6.4%?
2. What is the total interest paid over the loan period for both scenarios?
3. How does the length of the amortization period affect monthly repayments?
4. What would be the impact of a higher or lower loan amount on the monthly payments?
5. Can the couple reduce their payments by making early repayments?

**Tip:** Reducing your loan term or increasing monthly payments can significantly reduce total interest paid.

A Sydney couple had considered buying a house back in 2020 when home loans could have been had at an APR of 2.5%. Unfortunately, they did not have the necessary down payment at the time. Now, they finally have saved up the down payment, but home loans more likely come with an interest rate of 6.4% now. Assume a loan amount of A$1.8 million and an amortization period of 25 years at both points in time. What would have been the monthly loan repayment in 2020?

Find out the monthly loan repayment for a A$1.8 million mortgage at a 2.5% APR over 25 years. Using the loan amortization formula, we calculate the monthly payment with detailed steps. This solution is ideal for those learning about loans, interest rates, and amortization schedules.

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