Chapter 3 Exercises 1. You want to set up a perpetuity such that you will be paid $50,000 per year and you will make your first withdrawal at the end of the first year. A. If you find an account that earns 5% annual effective interest, how much will you have to deposit in this account? B. If you find an account that earns 4% annual effective interest, how much will you have to deposit in this account? C. If you find an account that earns 5% annual effective interest, but you predict that it will drop to 4% annual effective interest in 10 years, how much will you have to deposit in this account? 2. A financial services firm is trying to value a series of investment options for clients and has come to you for help. To do this, they would like to know the present value (how much they can/should charge) for a series of different investment options they would like to offer. Find the present value of each of the following: A. A $60,000 payment in 1 year at 5% annual effective interest. B. Two $30,000 payments, one at the end of year 1 and one at the end of year 2 at 6% effective annual interest. C. Six $10,000 payments, one at the end of each of the next 6 years at 5.5% effective interest. D. $1,000 payments at the end of each month for the next 5 years at an annual nominal interest rate of 6% with monthly compounding. E. A $40,000 payment at the end of year 1 , an additional deposit of $20,000 into the fund by the investor at the end of year 2 , and a payment of $40,000 at the end of year 4 at 6% effective annual interest. 3. What is the present value of a perpetuity that pays out $100 every two years, starting two years from today, assuming 5% effective annual interest? 4. To purchase a perpetuity paying $1000 per year with the first payment due at the end of year 11 , two payment options are presented. (i) Pay $900 per year at the end of each year for 10 years. (ii) Pay $X per year at the end of each year for the first 5 years and nothing afterwards. Calculate X