ANNUITIES

At some point of your life, you may have had to make a series of fixed payments over a period of time- such as rent or car payment- or have received a series of payments over a period time, such as bond coupons. These are called annuities. If you under stand the time value of money and have an understanding of the future and present value, it would be easy to understand annuities.
The most common famous frequencies are yearly, semi-annually, quarterly and monthly. There are two basic types of annuities : ordinary annuities and annuities due
Ordinary annuities: Payment are required at the end of each period, For an illustration, straight bonds usually make coupon payments at the end of every six months until the bond's maturity date
Future Value of Ordinary Annuity = C*[{(1+i)^n-1}/i]
Present Value of Ordinary Annuity = C*[{(1+r)^n-1}/r(1+r)^n]

C = Cash flow per period
i = Interest rate
n = number of payment


Annuity Due: Payment are required at the beginning of each period. rent is an illustration of annuity due. You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter.
Future Value of Annuity Due: = C*[{(1+r)^n-1}/i]*(1+i)
Present Value of Annuity Due: = C*[[(1+r)^n-1}/r(1+r)]*(1+r)

C = Cash flow per period
i = Interest rate
n = number of payment