Question

Best way to remember how to tell the difference between an ordinary annuity and annuity due when doing a problem? Also is it easier to just remember the formulas instead of looking at the tables?

Answer 1

Best way to remember the difference between an ordinary annuity and an annuity due is the timing of the payments. An ordinary annuity is paid at the end of the payment period, while an annuity due is paid at the start of the payment period.

An annuity is a series of payments at a regular interval, such as weekly, monthly or yearly. The payments in an ordinary annuity occur at the end of each period. In contrast, an annuity due features payments occurring at the beginning of each period.The example of an annuity due is rent. Ordinarily, rent is paid on the first of each month. This qualifies as an annuity due because the payments occur at a regular interval (monthly) and at the beginning of each period. Insurance premium payments are another common example of annuity due. While the examples of ordinary annuities are Housing loan, coupon bearing bonds, payment of mortgage etc, where the payment fall due at the end of each period.

To sum up, the payments made at the end of every period are called ordinary annuity. This is because ordinary annuity is the usual state of affairs. Usually all annuities are paid at the end of the period. And, when annuity payments are made in advance, we call them annuity due.

The difference in the formula to calculate the two different types of annuities is very small. The Present value formulas for both the annuities is given below.

Formula for ordinary annuity is : P * ( 1- (1+ r)^-n / r ), where , P is the annual payment, r is the discount rate used and n is the time period.

Formula for annuity due is : P * ( 1- (1+ r)^{-(n - 1)} / r ), where , P is the annual payment, r is the discount rate used and n is the time period.

As we can see that ordinary annuity payments are made at the end of each period whereas the payments for annuity due are made at the beginning of each period. Hence, the difference between ordinary annuity and annuity due is one extra period. Thus, an adjustment needs to be made for this one extra period while calculating both the present value and future value of an annuity due.

So, the difference between the formulas is for 1 extra period i.e -(n-1) , as can be seen in the annuity due formula.