Present Value of an Ordinary Annuity Calculation Examples Help

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Understanding the concept of Present Value of an Ordinary Annuity Calculation Examples

 

An ordinary annuity is a series of equal payments, with all payments being made at the end of each successive period.We calculate present value for an ordinary annuity to determine the total cost of an annuity if the payment is to be made right now.
The present value of an ordinary annuity can be calculated using following formula
 

P = PMT [(1 – (1 / (1 + r)n)) / r]
Where:
P = The present value of the annuity stream to be paid in the future
PMT = The amount of each annuity payment
r = The interest rate
n = The number of periods over which payments are to be made
 

Present Value of an Ordinary Annuity Calculation Examples Explanation

 

Let’s understand the concept with the help of following illustration.
 

Example 1: Calculate the present value on Jan 1, 2011 of an annuity of $500 paid at the end of each month of the calendar year 2011. The annual interest rate is 12%.
 

Solution: We have,
Periodic Payment R = $500
Number of Periods n = 12
Interest Rate i = 12%/12 = 1%
Present Value PV = $500 × (1-(1+1%)^(-12))/1%
= $500 × (1-1.01^-12)/1%
= $500 × (1-0.88745)/1%
= $500 × 0.11255/1%
= $500 × 11.255
= $5,627.54
 

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