Annuity and Types of Annuity - (TVM)

Annuity

An annuity is a stream of equal periodic cash flows over a specified time period.
These cash flows can be inflows of returns earned on investments or outflows of funds invested to earn future returns.


Simply, we can say an Annuity is a series of payments made at equal intervals.

Types of Annuity

There are two basic types of annuities.These are-

1)Ordinary Annuity
2)Annuity Due
Ordinary Annuity

An ordinary annuity is an annuity for which the cash flow occurs at the end of each period.



How can we determine Ordinary Annuity in math

Generally, we can see One year from now, Be Starting from next year, At the end of each period.



Formula of Ordinary Annuity

Ordinary Annuity(In case of compounding)

Ordinary Annuity



MATH

Present Value of Annuity

Case     Amount of Annuity   Interest Rate  Period

 A            $2500                            8%              10

Future Value of Annuity

Case     Amount of Annuity   Interest Rate  Period

  B            $11,500                         9%               8


Solution:

In case of  A

Given that,   Annuity, A= $2500
              Interest Rate, i = 8% or 0.08
                         Period, n=10
Present Value of Annuity, PV_A =?

      Now,
          

                                                                                                












Hence, the present value of  an annuity is $16,875.





In case of  B

Given that, 
                               Annuity, A= $11500
                        Interest Rate, i = 9% or 0.09
                                  Period, n=8
Future Value of Annuity, FV_A =?

Hence, the future value of an annuity is $126,827.




Annuity Due

Annuity due is an annuity for which the cash flow occurs at the beginning of each period.


How can we determine Annuity due in Math

Generally, we can see Starting today, Starting from now, At the beginning of each period.


Formula of Annuity due

Annuity Due

Annuity Due (In case of Compounding)

# Math

Present Value of Annuity Due

Case     Amount of Annuity   Interest Rate  Period

 A            $2500                            8%              10

Future Value of Annuity Due

Case     Amount of Annuity   Interest Rate  Period

  B            $11,500                         9%               8

Solution:

In case of A

Given that, Annuity, A= $2500

           Interest Rate, i = 8% or 0.08

                     Period, n = 10

Present Value of Annuity Due, PVAd = ?

Present Value of Annuity Due

In case of B

Given that, Annuity, A= $11,500

           Interest Rate, i = 9% or 0.09

                     Period, n = 8

Future Value of Annuity Due, FVAd =?

Future Value of Annuity Due

                                Present Value of Perpetuity

A perpetuity is an annuity with an infinite life.
In other words, an annuity that never stops providing its holder with a cash flow at the end of each year.

For example, the right to receive  $1,500 at the end of each year forever.

Sometimes it is necessary to find the present value of a perpetuity.If a perpetuity pays an annual cash flow of A, starting one year from now, the present value of the cash flow stream is -

                        PV = A / i

Where, 
              Present Value = PV
                Interest Rate = i
                      Annuity  = A

 # If,
           An annual cash flow, A = $100 
                          interest rate,  i = 12 %
                 the number of years = forever
                                            PV =?

Solution:

                          PV = A / i
                                = $ 100 / 0.12
                                = $ 833.33