Compute the following: a. Future value of 10,000 at APR = 5% compound annually for 10 years. b. Future value of 10,000 at APR = 5% compound every six months for 10 years. c. Future value of 10,000 at APR = 5% compound every quarter for 10 years. d. Future value of 10,000 at APR = 5% compound every month for 10 years. e. Present value of 100,000 at APR = 8% compounded every six months for 5 years. f. Present value of 100,000 at APR = 8% compounded every month for 5 years. g. Present value of an annuity paying 1,000 at APR = 8% for 3 years. h. Present value at time zero of an annuity 500 paying APR = 10% at the end of year 6 for four years. i. Effective Annual Rate (EAR) from: APR = 10% compounded annually. APR = 10% compounded semi-annually. APR = 10% compounded quarterly. APR = 10% compounded monthly. j. Annual Percentage Rate from: EAR = 9% compounded annually. EAR = 9% compounded monthly. EAR = 9% compounded daily. Question 2 Compute the following: 1. The amount at the end of 300 days of $ 1,000 with an APR = 10%. 2. The present value of $ 1,000 in 40 days with an APR = 10%. 3. The Present value of a perpetuity delivering $ 100 and EAR = 8%. 4. The PV of a perpetuity delivering $ 100 growing at g = 5% and EAR = 10%. 5. The PV of an annuity paying $ 100 at the beginning of each year for 20 years, with APR = 5%. 6. The PV of an annuity paying $ 100 each year for 10 years and growing at a rate of 3% per year, with an APR = 8%. Question 3 You are 60 years old and about to retire and you have a retirement plan so that at the end of each month you will receive $ 1,000 a month for the next 20 years. Assume that APR=6%. Assume now that the expected inflation is equal to 2%. What is the value of your retirement plan? 1 Unless differently stated, payments are assumed to occur at the end of each period.

Problem Set 2 Fabrizio Jacobellis SAIS Corporate Finance 2 Assume you are now 30 years old and at the age of 60 (30 years from now) you will benefit of the plan, what is the value of this retirement plan then, assume an average APR= 10% until you retire. Question 4 After SAIS you start working for a major company and you decide to start you retirement plan. You decide to put aside every six months $ 500, for the next 30 years. What is the FV of your retirement plan? Assume there is an APR = 12%. Consider now that there is a forecasted inflation rate of 2% per year, and you are still keen in putting aside $ 500 in real terms. How this would change your computations? Question 5 You want to give your daughter a gift of $ 100,000 when she finishes her college in 10 years from now. To do so you decide to invest today an amount in an asset paying interests every quarter, with an EAR = 10%. 1. Compute how much you have to invest today to guarantee $ 100,000. 2. Assume now that there is a tax on interest equal to 3%, re-do your computations. 3. Assume that a constant inflation rate of 2% is forecasted, and you are interested in ensuring the same purchasing power to your daughter, re-do your computations so that the amount you invest today would deliver the same purchasing power. Do the computations with and without taxes.