2 Annuity andRisk Perspectives p9-19年金计算.doc

Unit 2 Annuity and Risk Perspectives You might see a new finance outlet from annuity and risk perspectives. Annuity is the Archimedes Point in financial transaction, while risk measurement is the most effective way in evaluating a future trend. Dr. Xing The Sum of the First n Items of flat Ratio Series Remember that we have learned flat ratio in the first year of high school? (a) (b) (a)-(b), soon get (c) If q1, when , Formula (c) would save time in deriving many calculation formulae in TVM. The Future Value of an Annuity An annuity is a series of equal payments made at fixed intervals for special number of periods. If the payments occur at the end of each period, as they typically do, the annuity is an ordinary annuity. If the payments occur at the beginning of each period, it is called an annuity due. Without specified, annuity means ordinary annuity. The future value of an annuity, FVAn, is the total amount one would have at the end of the annuity period if each payment were invested at a given interest rate and held to the end of the annuity period. Defining FVAn is the future compound sum of an ordinary of n years, and PMT as the periodic payment, we can write Proof To get PMT from FVA, Example Calculate the future value of a 3-year, 5 percent annual rate of ordinary annuity of $100. The Future Value of Annuity due For an annuity due, each payment is compounded for one additional period, so the future value of the entire annuity is equal to the future value of an ordinary annuity compounded for one additional period. For annuity due, you might use the following formula. However, be sure not to confuse this formula with that of ordinary annuity. Example Calculate the future value of a 3-year, 5 percent annual interest rate annuity due of $100. The Present Value of an Annuity The present value of an annuity is the single (lump sum) payment today that would be equivalent to the annuity payments spread over the annuity per