Nine years ago, Ann entered into a $34,000 mortgage loan of 20 year and at a fixed rate of 12% p.a. (compounded monthly) with HSBC. Ann decides to refinance her loan with ANZ who offers 10% p.a. (compound monthly) for mortgage loan. There is no cost associated with this refinancing. What is her monthly savings from this refinancing?

To determine Ann's monthly savings from refinancing her loan, we need to go through the following steps:

### Step 1: Calculate Ann's original monthly payment with HSBC

Ann took a $34,000 mortgage loan with HSBC 9 years ago, for 20 years (240 months) at 12% p.a., compounded monthly. To calculate her monthly payment, we can use the standard amortization formula for monthly payments:

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

Where:
- $M$ = Monthly payment
- $P$ = Principal loan amount ($34,000)
- $r$ = Monthly interest rate (12% per annum compounded monthly, i.e., $ \frac{12}{12 \times 100} = 0.01 $)
- $n$ = Total number of months (20 years = 240 months)

Plugging in these values, we can calculate the monthly payment.

### Step 2: Calculate the remaining balance after 9 years

Ann has already paid for 9 years (108 months), so the remaining balance is the amount left to be paid after 108 months. This requires us to calculate the outstanding balance of her loan after making 108 payments.

The outstanding balance can be calculated using the following formula:

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

Where:
- $B$ = Remaining balance
- $P$ = Principal ($34,000)
- $r$ = Monthly interest rate (0.01)
- $n$ = Total number of months (240)
- $t$ = Number of months paid (108)

### Step 3: Calculate the new monthly payment with ANZ

Ann refinances her loan with ANZ, which offers 10% p.a. compounded monthly. The remaining balance (from Step 2) is the new loan amount. The new interest rate is 10% per annum compounded monthly, i.e., $ \frac{10}{12 \times 100} = 0.008333 $.

We will use the amortization formula again to calculate the new monthly payment, but this time using the remaining balance from Step 2, the new interest rate, and the remaining period (20 - 9 = 11 years, or 132 months).

### Step 4: Calculate the monthly savings

Finally, the monthly savings is the difference between Ann's original monthly payment and the new monthly payment.

Let's calculate each step.Here are the calculations based on the provided loan details:

1. **Original monthly payment (HSBC at 12%)**: \$374.37
2. **Remaining balance after 9 years**: \$27,370.42
3. **New monthly payment (ANZ at 10%)**: \$342.67
4. **Monthly savings from refinancing**: \$31.69

Thus, Ann's monthly savings from refinancing her mortgage with ANZ is approximately \$31.69.

Do you have any questions or would you like more details on any of these steps?

Here are 5 related questions you might find useful:
1. How is the monthly payment affected by changes in the interest rate?
2. What is the impact of early loan payments on overall interest savings?
3. How does compounding frequency affect the loan terms?
4. What are the long-term financial impacts of refinancing?
5. How does a fixed-rate mortgage compare to a variable-rate mortgage?

**Tip**: Refinancing to a lower interest rate earlier in the loan term typically results in greater savings.

Find out how to calculate the monthly savings from refinancing a $34,000 mortgage loan after 9 years, reducing the interest rate from 12% to 10%. Learn about key financial concepts like loan amortization, compound interest, and mortgage refinancing.

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