Annuity due and ordinary annuity are the two basic types of annuities. While ordinary annuity is an annuity for which one makes payment at the end of each interest period, annuity due is one for which someone makes payment at the beginning of each interest period. This section highlights the relationship between annuity due and ordinary annuity within the same period and same interest rate. The relationship between the two annuities can be best explained by use of a practical example. The first example is for an ordinary annuity while the second one is for annuity due.
If today is January 1 2008, and someone plans to make a series of four deposits over the next four years with each deposit being made at the end of every year, then this person will deposit the last amount on December 31, 2011.
However, if today is January 1, 2007 and another person preferred to deposit each amount at the beginning of years, for a period of five interest periods, and at the same interest rate as the first person, then he will deposit the last amount on January 1, 2011. While the depository dates are different in the two cases, withdrawal of the amount will take place on December 31, 2011 in both cases. Therefore, if the present day is December 31, 2011, then the values of the two annuities will be the same. Nonetheless, in ordinary annuity, the last deposit is made and withdrawn the same day. Therefore, the relationship is that, given the same period, the withdrawal, in both cases, will be made on the same day. Conclusively, it is necessary to note that, in ordinary annuity; the first withdrawal is made one period after the last deposit while, in annuity due; this payment is made immediately after the last deposit.