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?

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)

Key definitions

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

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

Continuous Annuity

Continuously compounding interest rate

The frequency of payments is infinite

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?

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

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

Perpetuities

Perpetuity – annuity that continues indefinitely

Same as annuities, there are perpetuities due, immediate and continuous

Varying annuities

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

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

Varying annuities

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

Varying Exercise

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