You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a **fully amortising** loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of **10**% pa and they have the same face value ($100) and maturity (3 years).

The only difference is that bond X and Y's **yields** are **8** and **12**% pa respectively. Which of the following statements is true?

A project's net present value (NPV) is negative. Select the most correct statement.

A furniture distributor offers credit to its customers. Customers are given 25 days to pay for their goods, but if they pay immediately they will get a 1% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or on the 25th day. All rates given below are effective annual rates.

Which of the below statements about effective rates and annualised percentage rates (APR's) is **NOT** correct?

Calculate the price of a newly issued **ten** year bond with a face value of $**100**, a yield of **8**% pa and a fixed coupon rate of **6**% pa, paid **semi**-annually. So there are two coupons per year, paid in arrears every six months.

A trader **sells** one crude oil European style **put** option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:

**Question 758** time calculation, fully amortising loan, no explanation

**Two** years ago you entered into a **fully amortising** home loan with a principal of $**1,000,000**, an interest rate of **6**% pa compounding monthly with a term of **25** years.

Then interest rates suddenly fall to **4.5**% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant.

**Question 921** utility, return distribution, log-normal distribution, arithmetic and geometric averages, no explanation

Who was the first theorist to propose the idea of ‘expected utility’?

**Question 925** mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, no explanation

The arithmetic average and standard deviation of returns on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 were calculated as follows:

###\bar{r}_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \ln \left( \dfrac{P_{t+1}}{P_t} \right) \right)} }{T} = \text{AALGDR} =0.0949=9.49\% \text{ pa}###

###\sigma_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \left( \ln \left( \dfrac{P_{t+1}}{P_t} \right) - \bar{r}_\text{yearly} \right)^2 \right)} }{T} = \text{SDLGDR} = 0.1692=16.92\text{ pp pa}###

Assume that the log gross discrete returns are normally distributed and that the above estimates are true population statistics, not sample statistics, so there is no standard error in the sample mean or standard deviation estimates. Also assume that the standardised normal Z-statistic corresponding to a one-tail probability of **2.5**% is exactly **-1.96**.

Which of the following statements is **NOT** correct? If you invested $1m today in the ASX200, then over the next 4 years: