Ordinary Annuity

Examples of annuities are common in our life like regular monthly utility bill payments, rent payments, dividend payments and loan installments whether to acquire a car or for other purposes. For an understanding of annuities and how their present and future values are calculated, you will need to understand the time value of money first.

What is an Ordinary Annuity?

An ordinary annuity consists of a stream of cash flows that are paid after the end of regular time period like regular monthly pension’s payments, quarterly interest payment on bond and annual dividend payments etc.

Formula

The present and future value formula for an ordinary annuity require following variables:

is cash payment during specific period of time

is interest rate during a period

is a total number of period

Present value annuity = P[1-(1+r)-n/r]

Future value annuity  =  P[(1+r)n-1/r]

Present Value of an Ordinary Annuity Example

You have inherited \$20,000 from your father and you wish to purchase a contract that will provide you a steady income for next 10 year. Currently, banks are paying 12% compound interest on the annual basis. How much would you be able to receive on yearly basis?

Solution:

We have,

Present Value (PV) = \$20,000

Number of period (n) = 10 year

Interest rate (r) = 12%

Present value annuity = P[1-(1+r)-n/r]

\$20,000 = P[1-(1+0.12)-10/0.12]

P = \$3540

Future Value of an Ordinary Annuity Example

You have travel enthusiasm and curious to visit Asia but cannot afford the lump sum amount of \$800. Currently, from your salary, you can save only \$150 per month and you are searching for a source which would provide you the sum after 5 years to enjoy a trip to Asia. For this, you consider buying an annuity contract with 7% interest rate annually.

Solution:

We have,

Monthly installments (P) = \$150

Number of period (n) = 5 year

Interest rate (r) = 7%

Future value annuity =  P[(1+r)n-1/r]

Future value annuity =  \$150 [(1+0.07)5-1/0.07]

Future value annuity = \$862.62