Lecture Practical business math procedures (11/e) - Chapter 13: Annuities and sinking funds

The main contents of the chapter consist of the following: Annuities: ordinary annuity and annuity due (find future value), present value of an ordinary annuity (find present value), sinking funds (find periodic payments).

Chapter Thirteen

Annuities and Sinking Funds

1. Differentiate between contingent annuities and annuities certain

2. Calculate the future value of an ordinary annuity and an annuity

due manually and by table lookup

LU13-1: Annuities: Ordinary Annuity and Annuity Due (Find Future

Value)

Learning unit objectives

LU 13-2: Present Value of an Ordinary Annuity (Find Present

Value)

1. Calculate the present value of an ordinary annuity by table

lookup and manually check the calculation

2. Compare the calculation of the present value of one lump

sum versus the present value of an ordinary annuity

LU 13-3: Sinking Funds (Find Periodic Payments)

1. Calculate the payment made at the end of each period

by table lookup

2. Check table lookup by using ordinary annuity table

Compounding Interest (Future Value)

Term of the annuity –

The time from the beginning of the first payment period to the end of

the last payment period

Future value of annuity –

The future dollar amount of a

Present value of an annuity – Tthe amount of money needed to

invest today in order to receive a

Annuity –

A series of payments

Classification of Annuities

Contingent annuities –

have no fixed number of

payments but depend on an

regular deposits/payments made

at the beginning of the period

Step 1 For period 1, no interest calculation is necessary, since money is

invested at the end of the period

Step 2 For period 2, calculate interest on the balance and add the

interest to the previous balance

Step 3 Add the additional investment at the end of period 2 to the new

Step 1 Calculate the number of periods and rate per period

Step 2 Look up the periods and rate in an ordinary annuity table The

intersection gives the table factor for the future value of $1

Step 3 Multiply the payment each period by the table factor This

gives the future value of the annuity

Calculating Future Value of an Ordinary

Annuity by Table Lookup

Future value of = Annuity payment x Ordinary

annuity ordinary annuity each period table factor

Calculating Future Value of an

Annuity Due Manually

Step 1 Calculate the interest on the balance for the period and add it to

the previous balance

Step 2 Add additional investment at the beginning of the period to the

new balance

Step 3 Repeat Steps 1 and 2 until the end of the desired period is

reached

Calculating Future Value of

an Annuity Due Manually

Find the value of an investment after 3 years for a $3,000

3,000.00

Beginning Yr 2 6,240.00

499.20

Yr 2 Interest 6,739.20

3,000.00

Beginning Yr 3 9,739.20

779.14

Yr 3 Interest

Calculating Future Value of an

Annuity Due by Table Lookup

Step 1 Calculate the number of periods and rate per period Add

one extra period

Step 2 Look up in an ordinary annuity table the periods and rate

The intersection gives the table factor for the future value

Future Value of an Annuity Due

Find the value of an investment after 3 years for a $3,000

annuity due at 8%.

Periods (N) = 3 x 1 = 3 + 1 = 4

4.5061 (table factor) x $3,000 = $13,518.30 Rate (R) = 8%/1 = 8%

$10,518.30

$13,518.30 $3,000 =

Calculating Present Value of an Ordinary

Annuity by Table Lookup

Step 1 Calculate the number of periods and rate per period

Step 2 Look up the periods and rate in the present value of an

annuity table The intersection gives the table factor for the present value of $1

Step 3 Multiply the withdrawal for each period by the table

factor This gives the present value of an ordinary annuity

Present value of Annuity Present value of ordinary annuity payment payment ordinary annuity table = x

Present Value of an Annuity

John Fitch wants to receive a $8,000

annuity in 3 years Interest on the annuity

is 8% semiannually John will make

withdrawals at the end of each year How

much must John invest today to receive a

stream of payments for 3 years

Lump Sums versus Annuities

John Sands made deposits of $200 to Floor Bank, which pays 8% interest

compounded annually After 5 years, John makes no more deposits What will be the balance in the account 6 years after the last deposit?

Future value of an annuity

Future value of a lump sum

R = 8%/2 = 4%

1.6010 (table factor) x $2,401.22 =

$3,844.35

Lump Sums versus Annuities

Mel Rich decided to retire in 8 years to New Mexico What amount must

Mel invest today so he will be able to withdraw $40,000 at the end of each

year 25 years after he retires? Assume Mel can invest money at 5% interest

Sinking Funds (Find Periodic Payments)

Sinking fund = Future x Sinking

fund payment value table factor

Sinking fund –

financial arrangement that sets aside regular periodic payments of a particular amount of money

SINKING FUND TABLE BASED ON $1