Each payment of an annuity due is compounded for one on ordinary annuity compounded for one The present value of an ordinary annuity, PVAN, is the vi intervals over the annuity period. The equation is: period, so the future value of an annuity due is equal to the future value of vation is: PVAordinarg(1+I) t would be equivalent to the annuity payments (PMT) recelved at fixed PVAN=PMT[11+m1] Many assets provide a serles of cash inflows over time; and many obligations require a series of payments. When the payments are equal and ore made at nxed Intervals, the series is an annuity. There are three types of annulties: (1) Ordinary (deferred) annulty, (2) Annulty 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 annulty. Growing annulties 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 ot the end of the annuity period if each payment (PMT) were invested at a given interest rate and heid to the end of the annuity period. The equation is: FVA=PMT[1(1+1)x1] Each payment of an annuity due is compounded for one period, so the future value of an annuity due is equal to the future value of an ordinary annulty compounded for one period. The equation is: FVAdue=FVAordinacr(1+I) The present value of an ordinary annuity, PVAN, is the value today that would be equivaient to the annuity payments (PMT) received at nxed intervals over the annulty period. The equation is: PVAN=PMT[11a+p1] Each payment of an annuity due is discounted for one period, so the present value of an annuity due is equal to the present value of an ordinary annuity multiplied by (1+1). The equation is: PVAdue=PVAondisary(1+I) One can solve for payments (PMT), periods (N), and interest rates (I) for annuitios, The easiest way to solve for these variables is with o financiol calculator or a spreadsheet. invested at a given interest rate and held to the end of the annuity period. The equation FVAN=PMT[I(1+I)N1] Each payment of an annuity due is compounded for one period, so the fut an ordinary annuity compounded for one period. The equation is: FVAdue=FVAordinary(1+ The present value of an ordinary annuity, value today that would be equiv intervals over the annuity period. The eqt PVAN=PMT[11(1+n)N1 Quantitative Problem 1: You plon to deposit $2,000 per year for 6 years into a money market account with an annual return of 3%. You plan to make your first deposit one year from todoy. a. What arnount will be in your eccount at the end of 6 years? Do not round intermediate calculations. Round your answer to the nearest cent. 5 b. Assume that your deposits wil begin today. What amount wili be in your account after 6 years? Do not round intermediate calculetions. Round your answer to the nearest cent. Quantitative Problem 2: You and your wife ore making plans for retirement: You plan on living 30 years after you retire and would like to have $95,000 annually an which to live. Your first withdrawal will be made one year after you retire and you anticipate that your rotirement account will earn 15% annually. a. What amount do you need in your retirement account the doy you retire? Do not round intermediate calculations, Round your answer to the nearest cent. 5 b. Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the dav vou retire? Do not round intermediate calculations. Round your answer to the nearest cent. 5 PVAN=PMT[I1(1+)N1] Each payment of an annuity due is discounted for one an ordinary annuity multiplied by (1+I). The equation One can solve for payments (PMT), periods (N), and in calculator or a spreadsheet. seriod, so the present value of an annuity due is PVA Ardinary(1+I) for annuities. The easiest way to solve for the: Quantitative Problem 1: You pian to deposit \$2,000 per year for 6 years into a money market account with an an make your first deposit one year from today
