Round off to two (2) decimal points for the calculation results. On top of correctness of the resulting computation and analysis, the tidiness and clarity of your presentation will also be considered in evaluating your answers. (a) Explain what annuity is and the differences between an ordinary annuity and an annuity due. What are the relationships of the present value and future value calculation of these two (2) types of annuities? (8 marks)

(b) Suppose you would like to buy a car using a loan that requires an annual payment of $1,000 for 20 years at the end of each year. If the annual interest rate is 3%, what are the present value of this car? What is the Excel function used for this calculation? What would the present value be if the loan requires a semi-annual payment of $500 at the beginning of each period? What is the Excel function for this annuity due? (5 marks)

(c) An investment promises to pay $500 each year for 15 years. Calculate the future value of this annuity under the following circumstances: Annual payment at the end of each year Quarterly payment at the end of each quarter Monthly payment at the end of each month Daily payment at the end of each day Create an Excel spreadsheet and specify the variable Annual interest rate r in Cell A1 and your choice of the rate value in Cell B1.

In following rows, use the Excel function to calculate the future value of each of the above annuity in Column B and display the function used in Column C.

If the number of payment per year is n, what is the Excel function used to calculate the future value of the annuity investment above? Draw a line chart in Excel showing the relationship between future value of this investment (Y-axis) and number of payment per year (X-axis). Let the Y-axis start from (minimum of Y-axis equal to) the value when n=1. What does the chart tell us? (12 marks)