Today is 1 July 2021. You are looking to purchase an investment property today (after months of research and negotiations). You have spoken to Peter, the loan specialist at Harrison Bank, to negotiate the terms of your mortgage. You and Peter have agreed to the following terms:

• You will borrow $700,000 today in order to purchase your chosen property.
• This mortgage will be repaid by level monthly repayments.
• Your first repayment to the bank will occur exactly 1 month from today, on 1 August 2021, and the final repayment will occur exactly 17 years from today, on 1 July 2038.
• Peter has arranged for an interest rate of 6.3% p.a. effective to be locked in for the life of this loan.

Using the information provided, answer the following questions. It is highly recommended you draw a diagram to represent the given information.

1. The first monthly repayment occurs on 1 August 2021, and the final monthly repayment occurs on 1 July 2038. How many repayments are there in this arrangement?

2. The interest rate for the loan is 6.3% p.a. effective. Calcualte the equivalent nominal annual rate compounding monthly. Give your answer as a percentage to 4 decimal places, and do NOT include a percentage sign.

3. Calculate the equivalent effective monthly rate. Give your answer as a percentage to 4 decimal places, and do NOT include a percentage sign

4. The last payment for the loan occurs on 1 July 2038. For the next question, we will refer to 2038 as the "final year". Type in the "final year" below (i.e. if the last payment occurs in 2031, type in 2031).

5. Calculate the size of the level monthly repayment needed in order to fully repay the loan by 1 July 2038. Give your answer to the nearest cent, and do NOT include a dollar sign.

6. Determine the value of 12L12.

7.

The interest rate for the loan is 6.3% p.a. effective. Which of the following is the best next step before trying to calculate the required monthly repayment for the mortgage?

a.

Convert the 6.3% to a nominal annual rate compounding monthly, and use this new rate directly to calculate the monthly repayments.

b.

Divide 6.3% by 12 to work in months

c.

No interest rate conversion is needed. The 6.3% can be used directly.

d.

Convert the 6.3% to an effective monthly rate, and use this rate directly to calculate the monthly repayments.

8.

In preparation of your tax return, you need to calculate the interest charged on your loan so that you can claim it as a tax deduction. Specifically, you are interested in the financial year ending 30 June 2022.

For the purposes of this question, pretend that the repayment on 1 July 2022 is occurring on 30 June 2022 so that there are 12 repayments made in this financial year.

Further, the subscripts used for loan outstanding are measured in months, e.g. 240L240 is the loan outstanding after 240 months/20 years.

In order to calculate the interest charged on the loan from 1 July 2021 to 30 June 2022, which value(s) of loan outstanding are needed?

a.

0L0, 1L1, and 12L12

b.

0L0 only

c.

0L0 and 12L12

d.

12L12 only

9.

What does the difference 012L0L12 represent?

a.

The principal repaid in the first year of the loan.

b.

The principal repaid in the first 12 years of the loan.

c.

The interest paid in the first year of the loan.

d.

None of the other choices are correct

10.

What does the product 1212L12i12 represent?

a.

Nothing. This expression is complete nonsense.

b.

The interest component of the 1212th repayment.

c.

The interest component of the 1313th repayment.

d.

The interest paid in the second year.