For dollar amounts, give your answer to the nearest cent and do not include any currency signs. For interest rates, give our answer as a percentage rounded to 2 decimal places and do not include a percentage sign. For example, if you get an answer of 1.234567%, you would enter 1.23 as your response.

For each question, some parts of the question may use values from earlier parts. In these cases, use the EXACT values from the earlier parts, not the rounded values.

For example, if you do the calculation in part a) and you get an answer of exactly $23.456, you would enter 23.46 as your response for part a). If part b) requires the answer from part a), then you would use 23.456 and not the rounded value.

Question 1

Geoffrey is the owner of a small grocery store, and is considering buying a car to help him transport his wares. He has found a suitable used car online that he was able to negotiate to a price of $26,000. After doing a bit more research, he has found the following additional expenses involved in the purchase:

• Insurance and registration will cost $530 per year, payable at the start of each year
• Based on mileage estimates, petrol will cost $220 per fortnight, payable at the end of each fortnight
• Servicing will cost $400 per year, payable at the end of each year (as the car was recently serviced by the previous owner

Assume that these are the only expenses involved with the purchase and operation of the car.

Geoffrey believes that the car can be used for 5 years before it will no longer be reliable, at which point he expects to sell it for a quarter of its current purchase price. He also has a business account at the bank that lets him borrow or invest money at 4.5% per annum effective.

(a) Calculate the present value of the running costs (i.e. the insurance and registration, the petrol, and the servicing).

(b) Calculate the present value of the sale price.

(c) What is the total cost of buying and running the car in today's dollars? Your answer should also take into account the eventual sale price.

(d) What is the equivalent monthly repayment over the next 5 years, where payments are made at the end of each month?