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

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Presentation on theme: "Dish of the day: annuity Designed and cooked by: Matt Fraser Yevgeniy Kalininskiy."— Presentation transcript:

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

2 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?

3 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)

4 Key definitions

5 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

6 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

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

8 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?

9 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,

10 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,

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

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

13 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,

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

15 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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