Annuities

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Annuities
Steven M. Foulks, CPA, CFP
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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

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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.

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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)

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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

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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?

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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.

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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.

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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!!

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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?

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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?