1. (Annuity - perpetuity) 3 years from now (at t=3) you will begin to receive cash flows of $1000 per year. These cash flows will continue forever. If the discount rate is 5%, what is the present value (now, at t=0) of these cash flows?
2. (Annuity) 6 years from now (at t=6) you will receive the first of 10 annual $10,000 payments. The current interest rate is 10%, but by the beginning of 6th year (at t=5), the rate will rise to 12%. What is the present value of this cash flow stream? (Hint: Break this into two stages -corresponding to the two time periods over which the different rates are in effect)
3. (Annuity ordinary/due) You are going to withdraw $40,000 at the beginning of each year for the next 5 years from an account that pays interest at a rate of 5%, compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much money will be in the account immediately before the 3rd withdrawal is made?
4. (Annuity - car loan) You wish to purchase a new Toyota Camry for an agreed upon price of $18,000. You will finance the entire new car purchase through your employer's credit union. You have been approved for a 48-month loan at an quoted rate (APR, monthly compounding) of 6.0%. What will be your monthly payment?
5. (Annuity - car loan) Assume that the car (in the above problem) is totaled in an accident exactly 2.5 years after purchase. According to the loan agreement, you must immediately pay off the remaining principal on the loan, if the car is totaled. Assume that the 30th monthly payment was originally due to be paid immediately after the wreck. How much do you owe on the car loan? (Hint: Think carefully about the timing of that 30th payment - and how that affects your calculation of the remaining principal)
6. (Annuity - credit card) You have a $10,000 balance on your credit card. The interest rate (APR, monthly compounding) on the card is 24%. If you make "minimum monthly payments" of $210, how long will it take you to pay off the credit card balance?
7. (Annuity - saving for future income) For some reason, you decide to enter law school exactly four years from today. You decide to begin saving for law school and wish to begin contributing monthly to an investment account earning 6% (APR, monthly compounding), to cover your law school tuition. The first savings contribution occurs one month from now and the last contribution occurs at the end of four years. Immediately upon beginning school, you will place your savings in a more conservative account earning 2% (compounded semi-annually). In order to pay your tuition, you will need to withdraw $10,000 from that account at the beginning of each six-month period for the three years (that you are in school). What is the size of the monthly contribution to savings (while working) that will exactly cover your withdrawal needs for the duration of law school? How would that monthly savings contribution change if you made all of contributions at the beginning of each month, starting today (at t=0)?
8. (Zero-Coupon Bond Pricing - Lump-Sum Problem) You are considering the purchase of a zero-coupon bond, which has 12 years to maturity and a face value of $100,000. If the yield-to-maturity (YTM) is 4%, what is a fair price for the bond? (Assume annually compounded interest)
9. (Zero-Coupon Bond Yield - Lump-Sum Problem) A 20-year zero-coupon bond with a face value of $100, sells for $50. What is the bond's yield-to-maturity? (Assume annually compounded interest)