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 $520,000 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 30 years from today, on 1 July 2051.
• Peter has arranged for an interest rate of 5% 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.

The first monthly repayment occurs on 1 August 2021, and the final monthly repayment occurs on 1 July 2051. How many repayments are there in this arrangement?

1. The last payment for the loan occurs on 1 July 2051. For the next question, we will refer to 2051 as the "final year". Type in the "final year" below (i.e. if the last payment occurs in 2031, type in 2031).

2. Determine the value of L12L12. Give your answer to the nearest cent, and do NOT include a dollar sign.

3. The interest rate for the loan is 5% p.a. effective. Which of the following is the best next step before trying to calculate the required monthly repayment for the mortgage?

4.

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. L240L240 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.

L0L0 and L12L12

b.

L12L12 only

c.

L0L0, L1L1, and L12L12

d.

L0L0 only

5.

What does the difference L0L12L0L12 represent?

a.

The interest paid in the first year of the loan.

b.

The principal repaid in the first year of the loan.

c.

None of the other choices are correct

d.

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

6.

What does the product L12i12L12i12 represent?

a.

The interest component of the 12th12th repayment.

b.

The interest paid in the second year.

c.

The interest component of the 13th13th repayment.

d.

Nothing. This expression is complete nonsense.

7. The first repayment of the loan occurs on 1 August 2021, and the final repayment occurs on 1 July in the "final year" as above. For each formula named below, select the corresponding valuation date (i.e. the point in time when the formula lands you)

PV ordinary annuity	Answer 1Choose...1 June in the "final year"1 June 20211 August 20201 July in the "final year"1 August 20211 July 20201 August in the "final year"1 July 2021
FV ordinary annuity	Answer 2Choose...1 June in the "final year"1 June 20211 August 20201 July in the "final year"1 August 20211 July 20201 August in the "final year"1 July 2021
PV annuity due	Answer 3Choose...1 June in the "final year"1 June 20211 August 20201 July in the "final year"1 August 20211 July 20201 August in the "final year"1 July 2021
FV annuity due