UGBA103_PS2_Solutions

UGBA103_PS2_Solutions - UGBA 103 Spring 2011 Solution to...

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UGBA 103 – Spring 2011 Solution to Problem Set #2 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 61 24 4 of 2 years, using our rule 1 4 1 0.2 1.0466 So the equivalent 6 month rate is 4.66%. b. Since one year is half of 2 years 1 2 1.2 1.0954 So the equivalent 1 year rate is 9.54%. c. Since one month is 1 24 of 2 years, using our rule 1 24 1 0.2 1.00763 So the equivalent 1 month rate is 0.763%. 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.) For a $1 invested in an account with 10% APR with monthly compounding you will have 12 0.1 1 $1.10471 12 So the EAR is 10.471%. For a $1 invested in an account with 10% APR with annual compounding you will have 1 0.1 $1.10 So the EAR is 10%. For a $1 invested in an account with 9% APR with daily compounding you will have 365 0.09 1 1.09416 365 So the EAR is 9.416%. 5-6. Your bank account pays interest with an EAR of 5%. What is the APR quote for this account based on semiannual compounding? What is the APR with monthly compounding? Using the formula for converting from an EAR to an APR quote
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k APR 1 1.05 k Solving for the APR 1 k APR 1.05 1 k With annual payments k = 1, so APR = 5% With semiannual payments k = 2, so APR = 4.939% With monthly payments k = 12, so APR = 4.889% 5-9. Suppose you invest $100 in a bank account, and five years later it has grown to $134.39. a. What APR did you receive, if the interest was compounded semiannually?
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UGBA103_PS2_Solutions - UGBA 103 Spring 2011 Solution to...

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