1. Less or Additional

2. Less or Additional

3. Less or Additional

Many assets provide a series of cash inflows over time; and many obligations require a series of payments. When the payments are equal and are made at fixed intervals, the series is an annuity. There are three types of annuities: (1) Ordinary (deferred) annuity, (2) Annuity due, and (3) Growing annuity. 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 used in the area of financial planning. Their analysis is more complex and often easier solved using a financial spreadsheet, so we will limit our discussion here to the first two types of annuities. The future value of an ordinary annuity, 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 held to the end of the annuity period. The equation is: (1 + I)N- 1 FVAN = PMT PMT I Each payment of an annuity due is compounded for one -Select- period, so the future value of an annuity due is equal to the future value of an ordinary annuity compounded for one -Select- period. The equation is: FVAdue = FVA ordinary (1 + I) The present value of an ordinary annuity, PVAN, is the value today that would be equivalent to the annuity payments (PMT) received at fixed intervals over the annuity period. The equation is: 1 1- PVAN = PMT PMT (1+1)N I period, so the present value of an annuity due is equal to the present value of an ordinary annuity multiplied by (1 + I). The Each payment of an annuity due is discounted for one -Select- equation is: PVA due = PVA ordinary (1 + I) One can solve for payments (PMT), periods (N), and interest rates (I) for annuities. The easiest way to solve for these variables is with a financial calculator or a spreadsheet