# Annuities and Capitalized Cost

**Annuity**

An annuity is a series of equal payments made at equal intervals of time. Financial activities like installment payments, monthly rentals, life-insurance premium, monthly retirement benefits, are familiar examples of annuity.

Annuity can be certain or uncertain. In *annuity certain*, the specific amount of payments are set to begin and end at a specific length of time. A good example of annuity certain is the monthly payments of a car loan where the amount and number of payments are known. In *annuity uncertain*, the annuitant may be paid according to certain event. Example of annuity uncertain is life and accident insurance. In this example, the start of payment is not known and the amount of payment is dependent to which event.

Annuity certain can be classified into two, *simple annuity* and *general annuity*. In simple annuity, the payment period is the same as the interest period, which means that if the payment is made monthly the conversion of money also occurs monthly. In general annuity, the payment period is not the same as the interest period. There are many situations where the payment for example is made quarterly but the money compounds in another period, say monthly. To deal with general annuity, we can convert it to simple annuity by making the payment period the same as the compounding period by the concept of effective rates.

**Elements of Annuity**

*A* = amount of periodic payment

*P* = present amount of all periodic payments

*F* = future worth of all periodic payments after the last payment is made

*i* = interest rate per compounding period

*n* = total number of payments

*m* = nominal rate (see compounded interest)

*t* = number of years