1. Assume that you have just turned 35 years old and recently welcomed your first child. In order to celebrate this occasion you decide to start saving for your child's education and for your retirement. You decide to kick off the savings with 6500 in one year from today. Beyond that point, because of increasing family expenses, savings will decline with a rate of 3% per year. Assume that you will only be able to save until the age of 65 at which point you retire. Your child will go to college as soon as she turns 18 years old and you estimate her total annual expenses to be 15,000 per year for 4 years. Once she graduates she will be financially self- sufficient and will not need further financial support. Finally assume that your life expectancy is 80 years and that you want to finance your retirement years with your savings. However, during your retirement years, the economy will suffer from inflation of 1.5% per year and the purchasing power of money will decrease. Answer ALL the following questions assuming that the nominal annual interest rate is 5% for all time periods. a. Calculate the present value (PV) of your savings for the period that starts today and ends when you retire. [5 marks] b. Calculate the present value (PV) of your child's expenses. Hint: Assume that your child's yearly expenses are paid at the end of each year. [5 marks] c. Calculate the future value (FV) of your savings when you reach retirement after paying your child's expenses. [4 marks] MANG6023W1 d. Calculate the inflation-adjusted (real) rate of return. [2 marks] e. Find the annual real amount of money that you will be living with during your retirement years. [4 marks] f. Define and critically discuss the concept of inflation and explain the difference between nominal and real interest rates. Based on your answer to (e) discuss how you expect the money you will be living with during your retirement years to fluctuate in () real values and (ii) nominal values. [30 marks] Page 2 of 6 1. Assume that you have just turned 35 years old and recently welcomed your first child. In order to celebrate this occasion you decide to start saving for your child's education and for your retirement. You decide to kick off the savings with 6500 in one year from today. Beyond that point, because of increasing family expenses, savings will decline with a rate of 3% per year. Assume that you will only be able to save until the age of 65 at which point you retire. Your child will go to college as soon as she turns 18 years old and you estimate her total annual expenses to be 15,000 per year for 4 years. Once she graduates she will be financially self- sufficient and will not need further financial support. Finally assume that your life expectancy is 80 years and that you want to finance your retirement years with your savings. However, during your retirement years, the economy will suffer from inflation of 1.5% per year and the purchasing power of money will decrease. Answer ALL the following questions assuming that the nominal annual interest rate is 5% for all time periods. a. Calculate the present value (PV) of your savings for the period that starts today and ends when you retire. [5 marks] b. Calculate the present value (PV) of your child's expenses. Hint: Assume that your child's yearly expenses are paid at the end of each year. [5 marks] c. Calculate the future value (FV) of your savings when you reach retirement after paying your child's expenses. [4 marks] MANG6023W1 d. Calculate the inflation-adjusted (real) rate of return. [2 marks] e. Find the annual real amount of money that you will be living with during your retirement years. [4 marks] f. Define and critically discuss the concept of inflation and explain the difference between nominal and real interest rates. Based on your answer to (e) discuss how you expect the money you will be living with during your retirement years to fluctuate in () real values and (ii) nominal values. [30 marks] Page 2 of 6