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Present Value of Ordinary Annuity:
The present value of an
ordinary annuity
is the
single sum
that, if
invested at compound interest now would provide for an annuity (a series of
withdrawals) for a certain number of future periods – the PV of an ordinary
annuity is the PV of a series of equal rents, to withdrawal at equal intervals
Example:
What is the PV of rental receipts of 6000 (Periodic Rent) each, to be received
at the end of each of the next 5 years (periods) when discounted at 12% (Int.
Rate)?
PV= Periodic Rent * (number from the table using 5 as N and .12 as I)
Present Value of an Annuity Due:
There are ALWAYS
one
fewer
discount period with annuities due compared
to an ordinary annuity – this is because you are making one pmt right at the
beginning –
to find the PV of an annuity due factor, multiply the PV of
an ordinary annuity by 1 + the interest rate
Examples of Present Value Ordinary Annuity Problems:
1.
Computation of the Present Value of Ordinary Annuity
You have just won a lottery totaling 4,000,000 – you will receive a check in
the amount of 200,000 at the end of each of the next 20 years – what is the
amount you have really won??
This is asking for what is the present value of the 200,000 checks you will
receive over that next 20? (Assume appropriate int rate of 10%)
You can calculate this in the following ways:
PV of Ordinary Annuity = Periodic Rent (200,000)* #from table (8.51356)
PV of Ordinary Annuity =
1,702,712
What this means is that the state can deposit 1,702,712 NOW and
earns 10% interest, it can withdraw 200,000 a year for 20 years to pay
you the 4,000,000 that you won.
2.
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 Spring '10
 Knight

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