Question

LG 5 P5-37 Compounding frequency, time value, and effective annual rates For each of the cases in the following table: a. Calculate the future value at the end of the specified deposit period. b. Determine the effective annual rate, EAR. c. Compare the nominal annual rate,r, to the effective annual rate, EAR. What re- lationship exists between compounding frequency and the nominal and effective annual rates? Case initial deposit Nominal annual rate, Compounding frequency, times/year) Deposit period years 6% $ 2,500 50,000 1,000 20,000

Answer 1

Case Ai Case Bo Deposit = $ 50,000 Deposit - $2500 IN Rate = 12 % N. Rate = 60% Compounding = 6 Compounding - 2 Duration - 3 yrs Duration - 5yrs 10 FV = 50,000 X (1+2%) FU = 2500 x (1 +3•7)" = $3359.79 Case D : Сое с: Deposit = $20,000 Deposit = $1,000 NRate = 16% NRate = 5% Compounding = 4 Compounding - 1 Duration - 6 yrs Duration = 10yrs 10 FU=20,0000 (1 + 4% FU = 1000 x (1 + 5%) Timex Compounding EU = Present Deposit X (1+ Nominal Rate) Compounding Times Nominal Rate 7 ULTIT Compounding a EAR = {1+ Nomin compounding Case A EAR = (1 + 6%) = 6.09% Case B EAR = (1+ 12%)" - = 12.61 % Cose C → EAR = (1 + 5%) - - 5% Case D EAR = 1 6. 98% a compounding - 1 2 2