Many assets provide a series of cash inflows over time; and mony obligations require a series of payments. When the payments are equal and are made at fixad interyals, the series is an aninulty. There are thiree types of annuities: (1) Ordinary (deferred) annuity. (2) Annuity due, and (3) Growing annulty, One can find an annuity's future. and present values, the interest rate built into annuity contracts, and the length of time it takes to reach a financial goal using an annuity, Growing annuities are often tised in the area of financial planning. Their analysis is more complex and often easier solved using a financial spreadsheet, so we will limit our diseussion here to the first two types of annuities. The future value of an ordinary annaity, FVAN, is the total amount one would have at the end of the annuity period if each payment (PMT) were invested at a given interest rate and heid to the end of the annulty period. The equation is: FVA=PMT[t(t+n4+1] Each pavment of an annuity due is compounded for one period, so the future value of an annuty due is equal to the future value of an ordinary annuity comgounded for one period. The equation is: FVAdin=FVAentlinay(1+1) The present value of an ordinary annuity, PVAr, is the value today that would be equlvalent to the annuity payments (PMT) received at fixed intervals over the annuity penod. The equation is: PVAX=PMT[11+1+081] Each payment of an annulty doe is discounted for one period, so the present value of an annuity due is equal to the present value of an ordinary annuify multiplied by (1+1). The equation is: PVAlos=PVAorliway(1+I)