Many assets provide a series of cash inflows over time; and many obligations require a series of payments. When the paryments are equal and are made at fored intervals, the series is an annuity. There are three types of annuities: (1) Ordinary (deferred) snnuity, (2) Annuity due, and (3) Growing annuity. One can find an annulty's future and present values, the interest rate built into annulty contracts, and the length of time it takes to reach a financial goal using an annuity. 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 annuries. The future value of an ordinary annuity, FVAn, is the total arnount 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 annuty period. The equation is: FVAAN=PMT[1(1+n+1] Each payment of an annuly due is compounded for one period, so the future value of an annuity due is equal to the future value of an ordinary annuity compounded for one periad. The equation is: PVAdut=FVAvotinary(1+1) The present vatue of an ordinary annuity, PVAw, is the value today that would be equivalenc to the annuity payments (PMT) received at floced intervals over the annuity penod. The equation is: PVAx=PMT[111+x21]. Each paryment 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 annuty muthiplied by (1+1). The equation is: PVAtoe=PVAetinary(1+1) One can solve for payments (PMT), periods (N), and interest rates (1) for annualies. The easlest way to solve for these variables is with a financial calculator or a spreadsheet. Quantitative Problem 1: You plan to deposit $2,300 per year for 5 years into a money market account with an annual return of 2%, You plan to make your first deposit one year from today. a. What amoint will be in your account at the end of 5 years? Do not round intermediate calculations, Round your answer to the nearest cent. 5 b. Assume that your deposits wail begin today. What amount will be in your account after 5 years? Do not round intermediate calculations. Round your answer to the nearest cent. Quantitative Problem 2: You and your.wife are making plans for netirement. You plan on living 30 years after you retire and would like to have 595,000 annualiy on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 15% annually. a. What amount do vou need in your retirement account the day you retire? Do not round intermed ate 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 day you rebire? Do not round intermediate calculations. Round your answer to the nezrest cent. 3 Many assets provide a series of cash inflows over time; and many obligations require a series of payments. When the paryments are equal and are made at fored intervals, the series is an annuity. There are three types of annuities: (1) Ordinary (deferred) snnuity, (2) Annuity due, and (3) Growing annuity. One can find an annulty's future and present values, the interest rate built into annulty contracts, and the length of time it takes to reach a financial goal using an annuity. 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 annuries. The future value of an ordinary annuity, FVAn, is the total arnount 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 annuty period. The equation is: FVAAN=PMT[1(1+n+1] Each payment of an annuly due is compounded for one period, so the future value of an annuity due is equal to the future value of an ordinary annuity compounded for one periad. The equation is: PVAdut=FVAvotinary(1+1) The present vatue of an ordinary annuity, PVAw, is the value today that would be equivalenc to the annuity payments (PMT) received at floced intervals over the annuity penod. The equation is: PVAx=PMT[111+x21]. Each paryment 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 annuty muthiplied by (1+1). The equation is: PVAtoe=PVAetinary(1+1) One can solve for payments (PMT), periods (N), and interest rates (1) for annualies. The easlest way to solve for these variables is with a financial calculator or a spreadsheet. Quantitative Problem 1: You plan to deposit $2,300 per year for 5 years into a money market account with an annual return of 2%, You plan to make your first deposit one year from today. a. What amoint will be in your account at the end of 5 years? Do not round intermediate calculations, Round your answer to the nearest cent. 5 b. Assume that your deposits wail begin today. What amount will be in your account after 5 years? Do not round intermediate calculations. Round your answer to the nearest cent. Quantitative Problem 2: You and your.wife are making plans for netirement. You plan on living 30 years after you retire and would like to have 595,000 annualiy on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 15% annually. a. What amount do vou need in your retirement account the day you retire? Do not round intermed ate 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 day you rebire? Do not round intermediate calculations. Round your answer to the nezrest cent. 3
