Hey I need help with question e and I have completed a through d. The following values have been calculated, assuming a discount rate of 8%:

a. present value of a perpetuity (also called a perpetual annuity) of $50 received each year at the end of each year

PV = 50 / 0.08 = $625

b. present value of an annuity of $50 received at the end of each year for 5 years

N = 5 I/Y = 8 PMT = -50.00 PV = 199.64

c. present value of an annuity of $50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6^th year

N = 10 I/Y = 8 PMT = -50.00 PV = 335.50

PV year 0 = $335.51 / (1.08)⁶ = 211.43

d. present value of a perpetuity of $50, with the first payment received at the end of the 16^th year

PV year 16 = $50 / 0.08 = $625

PV year 16 discounted to year 0 = $625 / (1.08)¹⁶ = $182.43

e. Show (with a time line, for example) that the perpetuity in a. is exactly the same as the sum of the annuities and perpetuities in b. to d.

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