Читать книгу Fundamentals of Financial Instruments - Sunil K. Parameswaran - Страница 104

An annuity is a series of payments made at equally spaced intervals of time. If all the payments are identical, then we term it as a Level Annuity. Examples include insurance premiums and monthly installments on housing loans and automobile loans, which are paid off by way of equal installments over a period of time.

If the first payment is made or received at the end of the first period, then we call it an ordinary annuity. Examples include salary, which will be paid only after an employee completes his duties for the month, and house rent, which will be usually paid by the tenant only at the end of the month. The interval between successive payments is called the payment period. We will assume that the payment period is the same as the interest conversion period. That is, if the annuity pays annually, we will assume annual compounding, whereas if it pays semiannually we will assume half-yearly compounding. This assumption is not mandatory and, in practice, we can easily handle cases where the payment period is longer than the interest conversion period, as well as instances where it is shorter.

Consider a level annuity that makes periodic payments of $A for N periods. On a timeline the cash flows can be depicted as shown in Figure 2.1. The point in time at which we are is depicted as time 0.

FIGURE 2.1 Timeline for an Annuity

Assume that the applicable interest rate per period is r%. We can then calculate the present and future values as shown here.