题目
Peter is given the opportunity to pay $100.00 in exchange for his choice of one of the following annuities: I. The first annuity pays $2.00 per month ($24.00 per annum) over the next five years when the discount rate is 12.0% per annum with monthly compound frequency II. The second annuity pays $18.00 per year over the next ten years when the discount rate is 12.0% annum with annual compound frequency Both annuities pay in arrears; that is, respectively, at the end of each month and at the end of each year. Assuming Peter's discount rate of 12.0% is a flat curve (i.e., insensitive to maturity) and fully reflects his risk preferences, which of the following statements is TRUE?
选项
A.Neither is worth the cost (the present value of both is below $100.00)
B.The monthly annuity is worth more than the annual annuity
C.The annual annuity is worth more than the monthly annuity
D.Both are worth the cost (the present value of both is above $100.00)
答案
C
解析
the present value (PV) of a stream of $1.00 payments over an annuity of (T) periods is given by A(T) = 1/y ×[1 - 1/(1+y/k)^(k×T)]. Therefore, The PV of the monthly annuity is equal to 1/0.120 ×[1 - 1/(1+0.120/12)^(12×5)]×$24.00 = $89.10, and The PV of the annual annuity is equal to 1/0.120 ×[1 - 1/(1+0.120/1)^(1×10)]×$18.00 = 1/0.120×[1 - 1/(1.120^10)]×$18.00 = $101.704 年金为的$ 1.00付款流的现值（PV）在T时段中是A(T) = 1/y ×[1-1/(1 y/k)^(k×T)]， 因此，每月年金的现值等于：1/0.120 ×[1-1/(1 0.120/12)^(12×5)]×$24.00 = $89.10。 每年年金的现值等于：1/0.120 ×[1-1/(1 0.120/1)^(1×10)]×$18.00 = 1/0.120×[1-1/(1.120^10)]×$18.00 = $101.704。