Question

Explain the difference between an ordinary annuity and an annuity due.

Answer 1

The difference between ordinary annuity and annuity due is illustrated as shown below:

Ordinary annuity can be defined as an annuity in which the payments occurs at the end of the period. In contrast, annuity due is defined as an annuity in which the payments occurs at the beginning of each period.

As mentioned in the previous point that the annuity due is the annuity in which the payments occurs at the beginning of each period on account of which the present value of annuity due is always greater than the present value of ordinary annuity given the same payment amount, number of payments. The same is explained with the help of an example.

For example: If 5 payments of $ 1,000 to be received at 10% rate of interest, then the value of ordinary annuity and annuity due is computed as follows:

Annuity Due value is computed as follows:

= $ 1,000 + $ 1,000 / 1.10¹ + $ 1,000 / 1.10² +  $ 1,000 / 1.10³ +  $ 1,000 / 1.10⁴

= $ 4,170 Approximately

Ordinary annuity value is computed as follows:

= $ 1,000 / 1.10¹ + $ 1,000 / 1.10² +  $ 1,000 / 1.10³ +  $ 1,000 / 1.10⁴ + $ 1,000 / 1.10⁵

= $ 3,791 Approximately

As can be seen the value of annuity due is greater than the value of ordinary annuity.

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