Compounded value and compounded rate. a. What would be the compounded value of one dollar in three years if the annual interest rate is 3 percent in Year 1 and is expected to rise to 5 percent in Year 2 and 6 percent in Year 3? b. What constant annual interest rate would produce the same compounded value over three years? Alternative financing plans. You can purchase a car with one of the following two financing plans. You make a down payment of $12,000 and 36 monthly payments of $400 starting immediately. Alternatively, you can make 60 monthly payments of $492 starting next month without any down payment. Which plan offers a better deal if the interest rate is 6 percent? Annuity versus perpetuity. You have just read an advertisement stating, "Pay us $100 a year for the next text years and we will pay you $100 a year thereafter in perpetuity." If this is a fair deal what is the implied rate of interest? Valuing a loan. A company borrowed $10 million for five years from Atlantic Bank. The company pays Atlantic Bank a fixed annual rate of 8 percent and must pay back the $10 million loan at the end of the borrowing period. A year has passed since the loan was made and Atlantic Bank wants to sell the loan to Pacific Bank. a. If the interest rate is now 7 percent, what is the value of the loan? b. What would be the value of the loan if the company was paying the by 4 percent every six months instead of 8 percent per year? Perpetual cash flows. You are currently a member of a club whose annual membership fee is $2,000, fee is expected to increase by 3 percent per year. a. Would you buy for $65,000 a lifelong family membership to the club that passed down to your descendants? You can earn 6 percent on a long-term deposit. b. What discount rate would make you indifferent. c. What annual membership fees would make you indifferent? d. What lifelong membership price would make you indifferent