Present Value Annuity Tables - DOC by vrt15699

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```									Acct 414                                                               Prof. Teresa Gordon

Time Value of Money Formulas:
Types of problems
Single Sum. One sum (\$1) will be received or paid either in the

Present (Present Value of a Single Sum or PV)
Future (Future Value of a Single Sum or FV)

PV                                                                        FV

There will always be at least four variables in any present or future value problem. Three of
the four will be known and you will solve for the fourth.
Single sum problems:
n = number of compounding periods
i = interest rate
PV = Value today of a single sum (\$1)
FV = Value in the future of a single sum (\$1)

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Acct 414                                                                 Prof. Teresa Gordon

Types of Annuity Problems
Ordinary annuity (OA)

A series of equal payments (or rents) received or paid at the end of a period, assuming a
constant rate of interest.
PV-OA (Present value of an ordinary annuity)

PV-OA

PMT           PM         PMT   PMT   PMT   PMT       PMT       PMT
T

FV-OA (Future value of an ordinary annuity)

FV-OA

PMT           PM         PMT   PMT   PMT   PMT       PMT       PMT
T

A series of equal payments (or rents) received or paid at the beginning of a period,
assuming a constant rate of interest.
V-AD (future value of an annuity due)
V-AD (present value of an annuity due)

PV-AD (Present value of an ordinary annuity)

PMT         PMT         PMT          PMT   PMT   PMT    PMT       PMT

FV-AD (Future value of an ordinary annuity)

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Acct 414                                                               Prof. Teresa Gordon

PMT          PMT           PM         PMT   PMT   PMT   PMT     PMT
T

Annuity Due vs. Ordinary Annuity
The difference between an ordinary annuity and an annuity due is that:

Given the same i, n and periodic payment, the annuity due will always yield a
greater present value
(less interest removed)
and a
greater future value

There will always be at least four variables in any present or future value problem. Three of the
four will be known and you will solve for the fourth.
Annuity Problems:
n = number of payments or rents
i = interest rate
PMT = Periodic payment (rent) received or paid
And either:
FV of an annuity (OA or AD) = Value in the future of a series of future payments

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Acct 414                                                              Prof. Teresa Gordon

OR
PV of an annuity (OA or AD) = Value today of a series of payments in the future

Note: To convert answer into an annuity due, multiply by (1 + n)

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Acct 414                                          Prof. Teresa Gordon

Types of Annuity Problems

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Acct 414                                                            Prof. Teresa Gordon

Example Problems
Ordinary Annuity Example
Suppose I must make three payments of \$500, each at the end of each of the next three
years. The interest rate is 8%. How much should I set aside today to have the required
payments?

This is an ordinary annuity:

What if the first payment comes immediately instead of at the end of the first year, how
much would I need to set aside today in order to have the required payments?

This is an annuity due:

We can use one of the formulas to adjust the IF – the easiest to memorize is the “multiply
by (1+i)” rule:

Alternative adjustment to the IF table is even easier – at least if you write the method at the

Look up IF for (n-1) and add 1:

This second method is also the “logical” decision you would make from looking at the time-
line.

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Acct 414                                                            Prof. Teresa Gordon

EXAMPLE PROBLEMS
Deferred annuity:
Assume that you are to receive three payments of \$100 each beginning 3 years from now. What
is this series of payments worth using a 12% discount rate?
Draw time line:

Analyze time-line: remember to identify the ordinary annuity involved before deciding the
number of periods deferred.
Alternative 1 – Work as two part problem

Alternative 2 – Adjust the ordinary annuity table IF:
Look up PV-OA IF for (d+n) and then subtract the PV-OA IF for d

Alternative 3 – Adjust the ordinary annuity table IF:
Look up PV-OA IF for n and then multiply by the PV IF for d

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Acct 414                                                              Prof. Teresa Gordon

Using Time Value of Money Tables
Let “IF” (interest factor) stand for the number from the appropriate time value of money table for
n periods and interest rate “i”

PV of a lump sum = FV * IF                           {from PV of \$ table}
FV of a lump sum = PV * IF                           {from FV of \$ table}
PV of Ordinary Annuity = PMT * IF                    {from PV of ord. annuity table}
FV of Ordinary Annuity = PMT * IF                    {from FV of ord. annuity table}
PMT = (PV of Ordinary Annuity) / IF                  {from PV of ord. annuity table}
or      (FV of Ordinary Annuity) / IF      {from FV of ord. annuity table}

CONVERSION TO ANNUITY DUE:
To find IF for Future Value of an Annuity Due: Add one to the number of periods
and look up IF on table. Then subtract one from the interest factor listed.
To find IF for Present Value of an Annuity Due: Subtract one from the number of
periods and look up IF on table. Add one to the interest factor.
Or        look up the IF on the appropriate table and multiply by (1 + i).

CONVERSION TO DEFERRED ANNUITY
Let d = number of periods deferred and n = number of periodic payments
Look up (d+n) on the appropriate table. Look up d on the same table.
Subtract the smaller interest factor from the larger to get the deferred
annuity IF.
Or        look up interest factor for n periods on appropriate annuity table. Then look
up interest factor from the corresponding “lump sum” table for d. Multiply
the two interest factors together to get the deferred annuity IF.

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