Your friend Suzie has just started a new job as a salesperson for a range of financial products offered by Wagon Financial. To her surprise, customers of Wagon Financial ask her very technical questions about the products she sells. Whilst Suzie has worked in sales before, she is not familiar with the products and has asked for your help to better understand them.

The first product Suzie represents is a short term loan. Here, customers can borrow small amounts of money, and have some options for the amount of time to repay the loan. Based on Wagon Financials past experience, the most typical loan amount for customers of this service is $1,250. The table below shows the repayments for the loan term options available

Using the information provided, answer the following questions.

a) For each of the above loan term options, calculate the equivalent simple annual interest rate.

b) We see that each additional month will cost the borrower $50 in additional interest. Calculate the equivalent simple annual interest rate for this $50 per month.

c) For a loan of $1,250 with interest of $50 charged in the first month, calculate the equivalent compound effective annual interest rate.

d) You should find that your answer in part c) is larger than your answer in part b). By considering simple and compound interest rates, give an explanation of this difference.

\begin{tabular}{c|c|c} 2 months & 3 months & 4 months \\ \hline$1,600 & $1,650 & $1,700 \end{tabular} The second product Suzie represents is an annuity. The customers of this product are typically retirees that use their retirement savings to buy a steady income stream. Like before, there are a range of options for this product, but the most typical arrangement is as follows: - Customers buy this product on their 65th birthday when they retire. - The annuity will make 20 annual payments of $80,000. - The first annual payment of $80,000 will occur on the customer's 68th birthday (customers typically rely on their personal savings to travel for the first few years). - For this product, Wagon Financial can invest the customers' money at 12% per annum effective. Using the information provided, answer the following questions. e) What price should Wagon Financial charge for this product? (2 marks ) f) Suppose that Joseph, an existing customer of this product (with the arrangement specified above), has just received the fifth payment of this annuity. Using the prospective method, how much money does Wagon Financial need to have set aside today (immediately after the fifth payment is made) to be sure that they can afford to make all future payments to Joseph? NOTE: Calculations done with the retrospective method will not score any marks. (2 marks) g) Suppose that immediately after making the fifth payment to Joseph as described above, Wagon Financial also implements a new investment strategy which they believe will yield even higher investment returns than the original 12% per annum. Assuming this to be true, would Wagon Financial need to set aside more or less money than your answer in part f) to be sure that they can afford to make all future payments to Joseph? Justify your answer. (1 mark) h) BONUS QUESTION Joy is nearing retirement and is considering buying an annuity product from Wagon Financial. However, she is considering adding a clause that says she will only receive the annual $80,000 payment if she is alive at the time of the payment (up to a maximum of 20 payments). Other than this clause, the specifications for the annuity she is considering are exactly the same as described above. Should Joy expect the price for this product to be cheaper or more expensive by adding this clause? (1 mark)