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Dish of the day: annuity

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

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  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 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 = 3,574.224

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

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

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

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