Dish of the day: annuityIngredientsAnnuitiesKey definitionsAnnuities cont.Due and ImmediateContinuous AnnuityExerciseCalculator ExerciseExercise #2PerpetuitiesVarying annuitiesArithmetic ExcerciseSlide 14Varying ExerciseDish of the day: annuityDesigned and cooked by: Matt FraserYevgeniy KalininskiyIngredients Definition of annuity Finding PV and FVDifference between Due and ImmediateContinuous annuitySpecial kind of annuity: perpetuityExamples of annuities using calculatorQuestions?AnnuitiesA series of payments made at equal intervals of timeInterest rate - rate at which interest is paidPayment period – the interval between annuity paymentsPayment amount – amount paid at each payment period (not always constant)Key definitionsAnnuities cont.The present value of the annuity n = number of terms i = interest rate payable at the end of the periodAccumulated value of the annuityDue and ImmediateImmediate – an annuity under which payments of 1 are made at the end of each period for n periodsDue – an annuity in which payments are made at the beginning of each period for n periodsContinuous AnnuityContinuously compounding interest rateThe frequency of payments is infiniteExercisePayments of $100 at end of the year for 10 years at 8% effective interest rate. What is the PV? What is the FV?Calculator ExercisePayments of $100 at end of the year for 10 years at 8% effective interest rate. What is the PV? What is the FV?Clear TVMSet ENDPmt = 100 , N = 10 , I/Y = 8 , FV = 0 CPT PV = 671.008 Pmt = 100 , N = 10 , I/Y = 8 , PV = 0 CPT FV = 1,448.656Exercise #2You want to retire at 62 with $1 million in you IRA. You expect a 8% rate of return and you start investing on your 22 birthday and your last investment is on your 61st birthday. How much do you need to invest each year.Set to beginning N = 40 , I/Y = 8, PV = 0 , FV = 1 Mil , CPT PMT = 3,574.224PerpetuitiesPerpetuity – annuity that continues indefinitely Same as annuities, there are perpetuities due, immediate and continuousVarying annuitiesArithmetic varying annuities – annuities that increase or decrease by a fixed amountArithmetic Excercise1st payment of 1000 increases by 100 every year, i=8% , n=10. Find the PV.P = 1000 , Q = 100 PMT = P+Q/I , FV = -n*Q/I , N = 10 , I/Y=8 , CMP PV = 9,307.7628Varying annuitiesGeometric varying annuities – annuities that increase or decrease by a fixed percentVarying Exercise1st payment 1000 , payments decrease by 2% every period , i=8%, n=5. What is the PV of this
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