34. 3: Time Value of Money: Annuities Click here to read the eBook: Future Values Time Value of Money: Annuities Many assets provide a series of cash flows over time; and many abligations require a series of payments. When the payments are equal and are made at fixed interva's, the series is an annuity There are three types of annulties: (3) Ordinary (deferred) annulty, (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 used in the ares of financial planning. Their analysis is more complex and often easier solved using a financial spreadsheet, so we will imit our discussion here to the first two types of annuities The future value of an ordinary annulity, PVAN, is the total amount one would have at the end of the annuilty period if each paryment (PMT) were invested at a given interest race and held to the end of the annuity period. The equation is: AP Each peyment of an annuity due is compounded forloneSelect period, so the future value of an annuity due is equal to the future value of an ordinary annulty compounded for one Select t period. The equation is: 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 Each payment of an annuity due is discounted for one Seledt period, so the present value of an ansuity due is equal to the present value of an ordinary annuity multplied by (1 +I).The equation is One can solve for payments (PMT), periods (N), and interest rates (1) for annuities The easiest way to solve for these variables is with a financial calculator or a spreadsheet 5850 Quantitative Problem 1: You plan to deposit S 1,900 per year for 4 years into a money market account with an annual return of 2%. You plan to make your first depot one year to Timeout The present value of an ordinary annulity, PVAN, Is the value today that would be equivaient to the annuity payments (PMT) received at fixed intervals over the annuity period. The equation is PVAN- PMT Each payment of an annuity due is discounted for one Slt equation is period, so the present value of an annuity due is equal to the present value of an ordingry annuity multiplied by (1 1). The One can solve for payments (PMT), periods (N), and interest rates (1) for annuilties. The easiest way to solve for these variables is with a financial caleulator or a spreadsheet Quantitative Problem 1: You plan to deposit $1,900 per year for 4 yearsinto a money market account with an annual return of 2%. You plan to make your first depose one year from today. a. What amount will be in your account at the end of 4 years? Round your answer to the nearest cent. Do not round intermediate calculations b. Assume that your deposts will begin today. what amount will be in your account after 4 years? Round your answer to the nearest cent. Do not round intermediate calculations Quantitative Problem 2: You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $80,000 annualily on which to live. Your first withdrawal wil be made one year after you retire and you anticipate that your remere account wil earn 12% anualy a. what amount do you need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations b. Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do now reed in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations Contisue without seving