Why Present Value of "Annuity Due" higher than "Ordinary Annuity"?

Feb 8, 2013

Why Present Value of "Annuity Due" higher than "Ordinary Annuity"?

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Why is the present value of the annuity due higher than that of the ordinary annuity? To answer this question, let's look at the same time understanding the difference between these two annuities.
Annuity due is a fixed annuity payment stream which performed at the beginning of each period (annuity in advance). Example, You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter.

Ordinary annuity is a stream of fixed payments made at the end of each period of time (at the end of the annuity / annuity in arrears). For example, straight bonds usually pay coupon payments at the end of every six months until the bond's maturity date.

Because annuities due done early, then the due date of each payment will be accumulated each year. This means when we perform calculations with the present value (at the moment), then each annuity payment will usually be discounted for one year or less. This makes as the present value of an annuity due yield greater than ordinary annuity.

According to Investopedia.com, "The present value of an ordinary annuity is less than that of an annuity due because the further back of the discount by a future payment, the lower its present value: each payment or cash flow in ordinary annuity occurs one period further into future".

You can read more about  how to calculate the present and future values of you annuity here: http://www.investopedia.com/articles/03/101503.asp#ixzz2KKYBwpxR

I hope this post can help you.

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