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 = 671.008  Pmt = 100, N = 10, I/Y = 8, PV = 0 CPT FV = 1,448.656

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 = 3,574.224

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 = 9,307.7628

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?