Question 24(updated)

24. 3: Time Value of Money: Annuities Mamy assets provide a senes of cash infions over time; and mamy obligations require a series of payments. When the pavments are equal and are made at fixed interval, the senes is an annumy. There are three types of annuibess (1) Ordinary (deferred) annuity, (2) Annuity due, and (3) Grewing anmuity, One can find an annuty's future and preient values, the interest tate buit into annuity contracts, and the length of time it takes to reach a financial goal using an annuity. Grewing annuities are often used in the area of fnancill planning. Their analysis it more complex and often easier solved utiog a finandal spreadsheet, so we will timit our ditcusioo here to the fint two types of annuties: The future value of en ordinary annwity, FVha, is the total amount ene would have at the end of the annuily period if each payment (pMr) were invested at a given interast rate and. theld to the end of the annuity period. The equation is: Each payment of an annuity due is compounded for one for one period, The equation is: leriod, so the future value of an annuity due is equal to the future velue of an ortinary annuity compounded The present value of an ordinary annuhy, PVAw, is the value today that would be equivalent to the annulty payments (PMT) received at fived intervals over the annuity period. The equation is: PVAAN=PMT[113+e21] Each payment of an annuity die is discounted for one period, so the present value of an arnuty due is equal to the present value of an ordinary annuty multplied by (1+1). The equation is: PVAj==PVAeddang(1+1) One can solve tor payments (PMT), periods (N), and interest rates (t) for annuities. The easiest way to solve for these variables is with a financal caiculator or a spreadsheet. Quantitative Problem 1t You plan to deposit \$1,900 per year for 4 years into a money market account with an annual cetum of 2%, You plan to make your first deposi one year from today. PVAx=PMTT[11+(1+BN1] Each payment of an onnulty due is discounted for one (1+1). The equation is: period, so the present value of an annuity due is equal to the present value of an ordinary annuity multplied by PVAdou=PVAieliear(1+1) One can solve for payments (PMT), periods (N), and interest rates (1) for annuities. The easiest way to solve for these variables is with s financial calculater or a spreadsheet. Quantitative Problem 1: You pian to deposit \$1,900 per yeor for 4 years into a money market account with an annual retum of 246 . You plan to make your first deposit ane year from today, a. What amount will be in your account at the end of 4 years? Do not round intermediate caiculations. Round your answer to the nearest cent: b. Assume that your deposits will begin today. What amount will be in your account after 4 years? Do not round intermediate calculations. Found your answer to the nearest cent: 10 Quantitative Problem 2t You and your wife are making plans for retirement: You plan on living 25 years afer you retire and would like to hove 595 , 000 arnually on which to ilveYour first withdrawal will be made one year after you retire and you anticipate that your retirement account will eam 15% annually. a. What amcunt do you need in your retirement actount the doy you retire? Do not round intermediate calculations. Round your answer to the nearest cent. 3 D. Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do yeu now need in your retinement account the dar you retre? Dp nat raund intermed ate calculations, Round your answer to the nearest cent: 5