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what is an annuity

When the periodic cash flows are of the same amount, the pattern is defined as annuity, for example, pension payments, wages, rental and etc.


two basic types of annuities

Ordinary annuity: cash flows received/paid at the end of each period, such as
Mortgage repayments

Annuity due: cash flows received/paid at the beginning of each period, such as
Lease payments


ordinary annuity:
Kate is entitled to a retirement income stream which pays her $30,000 per annum for next 20 years. Assume interest rate is 10% per annum and the first payment is in one year. How much is this income stream worth in terms of PV?
Kate’s income stream matches the definition of ordinary annuity (periodic identical amount at the end of each period).

[2ndF] [CA] (clear up memory)
30,000 [PMT] (annuity)
10 [I/Y] (r in %)
20 [N] (# of periods)
0 [FV] (0 future value)
[COMP] [PV] (compute PV)
Display -255,406.91

= 255,406.91

How to interpret this present value, 255,406.91?
It is equivalent to those 20 annual payments @ 10% interest rate (discount rate).
Kate is indifferent from a) to receive $255,406.91 NOW or b) $30,000 p.a. at year-end for the next 20 years.
It also implies the financial institution promising her the income stream must have at least $255,406.91 under Kata’s name NOW.
If interest rate were 8%, should the financial institution have more or less money under Kata’s name


explain annuity due

The present value of an annuity due is equivalent to the present value of an ordinary annuity compounded one additional period.

The future value of an annuity due is equivalent to compounding by one additional period the future value of an ordinary annuity
FV of annuity due


explain amortization

Paying off debt with a fixed repayment schedule in regular instalments over a period of time.

i.e. mortgage repayment


explain a sinking fund

Sinking fund
Establishing a fund/reserve with a fixed payment schedule in regular instalments over a period of time.

i.e. saving plan for retirement; credit enhancement in bond contract (allocate funds to a trust for retiring the bond in the future)


explain a perpertuity

Perpetuity is a special ordinary annuity where the cash flows begins at the end of each period and continues perpetually (aka. to infinity).
Perpetuity has present value, but no future value (infinity).
PV of perpetuity formula can be derived from PV of ordinary annuity.


Sam receives a constant stream of cash flows worth $1,000 each year to infinity with the first payment made in one year. What is the present value of this income stream if the interest rate is 10% p.a.?
First payment is made in one year, PMT = 1,000

pv = pmt / r

pv = 1000/0.10 = 10,000


explaina growing perpertuity

Cash flows grow at a constant speed (rate) and continue perpetually.
CFk+1 = CFk × (1 + g)
Similar to perpetuity, growing perpetuity has no FV.
PV of growing perpetuity


do power point calcs and sem

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