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## Annuities

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Title: Annuities

1
Annuities
Steven M. Foulks, CPA, CFP
2
Introduction
• Annuity - a series of equal cash flows with equal
intervals between cash flows
• Most long ranged financial goals can only be
achieved by periodic investing. Annuity
computations help us solve these types of
problems

3
Vocabulary
• Ordinary annuity - an annuity with payments being
made at the the end of the time period
• Example - car loan payments
• Annuity due - an annuity with payments being made
at the the beginning of of the time period (i.e.,
First payment due immediately)
• Example - rent
• Compounding, unless otherwise stated, is equal to
the annuity time intervals. For example, if the
annuity call for monthly payments, compounding is
monthly.

4
Annuity problem solving steps
• 1st - Determine if the problem is a lump sum or
annuity problem. It might be a combination of
both.
• 2nd - Determine what variable you are being asked
to solve for. In our problems we will be solving
for only the PV, FV and A (the annuity)

5
Annuity problem solving steps
• 3rd - Determine the type of problem - PV, or FV.
If it is a PV problem you will either be given,
or asked to solve for PV, etc.
• 4th - determine if it is an - annuity due or
ordinary annuity problem.
• 5th - arrange the terms in the equation so that
the term you are solving for is isolated on one
side of the equality

6
Annuity example
• Assume that your daughter will marry in 15 years
and you plan an elaborate wedding. You feel that
it will probably cost 100,000. Starting today
you can invest an amount monthly in a diversified
portfolio of stocks earning 11 . How much must
you invest each period to accomplish your goal?

7
Example solution
• Step 1 - The problem is an annuity problem with a
series of payments required to fund your goal
• Step 2 - You are being asked to solve for the
annuity A in our formula) - How much must you
save each month?
• Step 3 - The problem is a future value problem.
You are given the future value.

8
Example solution
• Step 4 - The problem is an annuity due problem.
The first payment will be made immediately
• Step 5 - Isolate A on one side of the equality
and put the other terms o the other side.

9
Problems?
• The most difficult part of solving annuity
problems is determining step 3, Determine the
type of problem - PV, or FV
• If people are given lump sum and annuity problems
together they have great difficulty with step 1
as well!!

10
Examples
• Carlos Lavardo has saved 1 million for
retirement. If he earns 10 on his investments,
and expects to live 24 years in retirement, how
much can you withdraw monthly at the beginning of
each month?
• Loris Regiani wants to buy a new house in Chicago
which costs 1 million. Assuming he can make a
down payment of 100,000, how much will his
monthly payments be if he desires a 30 year loan
when interest rates are 5 ¾ percent?

11
Examples
• Ben Bostrum wants to accumulate 1.5 million in a
retirement fund by the age 55, how much must he
save each month, at the beginning of each month,
if he earns 10 on his money and he is currently
33 years old?