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:

**P **is cash payment during specific period of time

**r **is interest rate during a period

**n **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

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