Calculate the following values, 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 b. present value of an annuity of $50 received at the end of each year for 5 years 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 6th year d. present value of an annuity of $50, with the first payment received at the end of the 16th year 4.4 a. Show (with a time line, for example) that the perpetuity in 4.3a. is exactly the same as the sum of the annuities and perpetuities in 4.3b. to 4.3d. b. Show that their present values add up to the same amount.