"quantity"exercise:The Time Value of Money
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Questions 1:
The stated (quoted) annual interest rate on an automobile loan is 10%. The effective annual rate (EAR) of the loan is 10.47%. The frequency of compounding per year for the loan is closest to:
A、 quarterly.
B 、monthly.
C 、weekly
Questions 2:
A consultant starts a project today that will last for three years. Her compensation package includes the following:
If she expects to invest these amounts at an annual interest rate of 3%, compounded annually until her retirement 10 years from now, the value at the end of 10 years is closest to:
A 、$618,994.
B、 $566,466.
C、 $460,590
B is correct. EAR = (1 + Periodic interest rate)m – 1. The solution is found iteratively by substituting the possible frequency of compounding until the EAR is 10.47%. For weekly compounding, (1 + 0.10/52)52 – 1 = 0.10506 = 10.51%. For monthly compounding, (1 + 0.10/12)12 – 1 = 0.10471 = 10.47%. For quarterly compounding, (1 + 0.10/4)4 – 1 = 0.10381 = 10.38%. Thus, the correct answer is monthly compounding.
C is incorrect; (1 + 0.10/52)52 – 1 = 0.10506 = 10.51%
A is incorrect; (1 + 0.10/4)4 – 1 = 0.10381 = 10.38%
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