Chapter 5 : Interet rates
Page161
Interest rate quotes and adjustments
5-1. Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of
a. Six months.
b. One year.
c. One month.
a. Since 6 months is [pic] of 2 years, using our rule [pic]
So the equivalent 6 month rate is 4.66%.
b. Since one year is half of 2 years [pic]
So the equivalent 1 year rate is 9.54%.
c. Since one month is [pic] of 2 years, using our rule [pic]
So the equivalent 1 month rate is 0.763%.
5-2. Which do you prefer: a bank account that pays 5% per year (EAR) for three years or
a. An account that pays 2[pic] every six months*…show more content…*

9% APR rate compounded daily: earned annual rate = (1 + 0.09/365)^365 - 1 = 0.09416 = 9.416% Le même trouvé sur un autre site : 5.4. You have found three investment choices for a one-year deposit: 10% APR Compounded monthly, 10% APR compounded annually, and 9% APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year.) Sol: 1+EAR= (1+r/k)k So, for 10% APR compounded monthly, the EAR is 1+EAR= (1+0.1/12)12 = 1.10471 => EAR= 10.47% For 10% compounded annually, the EAR is 1+EAR= (1+0.1)=1.1 * EAR= 10% (remains the same). For 9% compounded daily 1+EAR= (1+0.09/365)365 = 1.09416 * EAR= 9.4% 5-5) je n’ai pas trouvé 5-7 ) Suppose the interest rate is 8% APR with monthly compounding. What is the present value of an annuity that pays $90 every 6 months for 5 years? This question is harder than it seems. The problem is that the payment period does not coincide with the interest period. So I will convert the 8% compounded monthly to a rate compounded semi-annually let the semiannual rate be j (1+j)^2 = (1.02)^4 1+j = (1.02)^2 = 1.0404 j = .0404 PV = 90(1 - 1.0404^-30)/.0404 = $ 1548.75 5-8. You can earn $50 in interest on a $1000 deposit for eight months. If the EAR is the same regardless of the length of the investment, how much interest will you earn on a $1000 deposit for a. 6 months. b. 1 year. c. 1 1/2

9% APR rate compounded daily: earned annual rate = (1 + 0.09/365)^365 - 1 = 0.09416 = 9.416% Le même trouvé sur un autre site : 5.4. You have found three investment choices for a one-year deposit: 10% APR Compounded monthly, 10% APR compounded annually, and 9% APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year.) Sol: 1+EAR= (1+r/k)k So, for 10% APR compounded monthly, the EAR is 1+EAR= (1+0.1/12)12 = 1.10471 => EAR= 10.47% For 10% compounded annually, the EAR is 1+EAR= (1+0.1)=1.1 * EAR= 10% (remains the same). For 9% compounded daily 1+EAR= (1+0.09/365)365 = 1.09416 * EAR= 9.4% 5-5) je n’ai pas trouvé 5-7 ) Suppose the interest rate is 8% APR with monthly compounding. What is the present value of an annuity that pays $90 every 6 months for 5 years? This question is harder than it seems. The problem is that the payment period does not coincide with the interest period. So I will convert the 8% compounded monthly to a rate compounded semi-annually let the semiannual rate be j (1+j)^2 = (1.02)^4 1+j = (1.02)^2 = 1.0404 j = .0404 PV = 90(1 - 1.0404^-30)/.0404 = $ 1548.75 5-8. You can earn $50 in interest on a $1000 deposit for eight months. If the EAR is the same regardless of the length of the investment, how much interest will you earn on a $1000 deposit for a. 6 months. b. 1 year. c. 1 1/2

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