e. Consider a 4-year amortizing loan. You borrow $10,000 initially and repay it in 4 equal annual year-end payments and the interest rate is 10%. i. What will be the annual payment? [2 marks] (You can use Excel or financial calculator to find annual payment) ii. Prepare the loan amortization schedule. [8 marks] (Hints: See the example of loan amortization in Table 5.5)

f. You are working as a financial planner. A couple has asked you to put together an investment plan for the education of their daughter Sophie. She is a bright seven-year- old (her birthday is today), and everyone hopes she will go to university after high school in 10 years, on her 17th birthday. You estimate that today the cost of a year of university is $16,000, including the cost of tuition, books, accommodation, food, and clothing. You forecast that the annual inflation rate will be 3%. You may assume that these costs are incurred at the start of each university year. A typical university program lasts 4 years. The effective annual nominal interest rate is 5%. Suppose the couple invests money on her birthday, starting today and ending one year before she starts university. How much must they invest each year to have money to send their daughter to university? [20 marks]

Hints: First find the annual cost of university in nominal terms. For example, the cost of a year of university one year from now will be $16000*(1+inflation rate)^1 = 16000*1.03=$16,480 and two year from now will be $16000*(1+inflation rate)^2 = 16000*1.03^2 = $16974.4. Once you find the annual cost of university for year 10, 11, 12 and 13, you can find the present value of these cash flows at year 10 using 5% discount rate. That is the money Sophie needs when she will start university on 17 th birthday and this amount should be equal to the future value of annuity, annual contribution made by Sophies parents. Now, given the future value of annuities (annuity due), find the annual contribution (PMT).