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Dish of the day: annuity Designed and cooked by: Matt Fraser Yevgeniy Kalininskiy

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Ingredients Definition of annuity Finding PV and FV Difference between Due and Immediate Continuous annuity Special kind of annuity: perpetuity Examples of annuities using calculator Questions?

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Annuities A series of payments made at equal intervals of time Interest rate - rate at which interest is paid Payment period – the interval between annuity payments Payment amount – amount paid at each payment period (not always constant)

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Key definitions

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Annuities cont. The present value of the annuity n = number of terms i = interest rate payable at the end of the period Accumulated value of the annuity

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Due and Immediate Immediate – an annuity under which payments of 1 are made at the end of each period for n periods Due – an annuity in which payments are made at the beginning of each period for n periods

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Continuous Annuity Continuously compounding interest rate The frequency of payments is infinite

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Exercise Payments of $100 at end of the year for 10 years at 8% effective interest rate. What is the PV? What is the FV?

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Calculator Exercise Payments of $100 at end of the year for 10 years at 8% effective interest rate. What is the PV? What is the FV? Clear TVM Set END Pmt = 100, N = 10, I/Y = 8, FV = 0 CPT PV = Pmt = 100, N = 10, I/Y = 8, PV = 0 CPT FV = 1,

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Exercise #2 You 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 61 st 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,

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Perpetuities Perpetuity – annuity that continues indefinitely Same as annuities, there are perpetuities due, immediate and continuous

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Varying annuities Arithmetic varying annuities – annuities that increase or decrease by a fixed amount

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Arithmetic Excercise 1 st 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,

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Varying annuities Geometric varying annuities – annuities that increase or decrease by a fixed percent

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Varying Exercise 1 st payment 1000, payments decrease by 2% every period, i=8%, n=5. What is the PV of this annuity?

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