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Annuities

Steven M. Foulks, CPA, CFP

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

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.

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)

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

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?

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.

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.

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!!

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?

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?