The document discusses annuities and their types. It defines an annuity as a series of equal periodic payments made at regular intervals. There are three types of annuities: certain annuity which has a fixed duration, perpetual annuity which has an indefinite duration, and contingent annuity whose duration depends on an event. Annuities can also be ordinary, where payments are made at the end of each period, or annuity due, where payments are made at the beginning of each period. The document also defines important terms like periodic payment, payment period, and term of an annuity. It explains the concepts of present value and future value of an annuity and includes formulae and sample problems.

1. Click to edit Master title style
1
Maths
Presentation
To p i c - A n n u i t i e s A n d E M I s
P u l k i t A g a r w a l
F Y B A F
R o l l N o - 5 8

2. Click to edit Master title style
2
ANNUITY AND ITS TYPES
• A series of equal periodic payments is called annuity. The payments
are of equal size and at equal time interval.
On the basis of the
closing of an annuity, there are three types of annuities:
• Certain Annuity:
Here the duration of the annuity is fixed (or certain), hence called
certain annuity.
• Perpetual Annuity:
Here the annuity has no closing duration, i.e. it has indefinite duration.
Practically there are rarely any perpetuities.
• Contingent Annuity:
Here the duration of the annuity depends on an event taking place. An
example of contingent annuity is life annuity. Here the payments are to
be done till a person is alive.
2

3. Click to edit Master title style
3
ANNUITY AND ITS TYPES
3
On the basis of when the periodic payments are made we have
two types
of annuities: ordinary annuity and annuity due.
• Immediate (Ordinary) Annuity:
The annuity which is paid at the end of each period is called
as immediate (ordinary) annuity. The period can be monthly,
quarterly or yearly etc. For example, stock dividends, salaries
etc.
• Annuity Due:
In an annuity due, by contrast, payments are made at the
beginning of each period.

4. Click to edit Master title style
4
TERMS OF IMPORTANCE:
4
• Periodic Payment:
The amount of payment made is called as periodic payment.
• Period of Payment:
The time interval between two payments of an annuity is called as
the
period of payment.
• Term of an annuity:
The time of the beginning of the first payment period to the end of
the last payment period is called as term of annuity. An annuity gets
matured at the end of its term.

5. Click to edit Master title style
5
Present Value
5
• The present value of an annuity refers to how much
money would be needed today to fund a series of
future annuity payments.
• Because of the time value of money, a sum of
money received today is worth more than the same
sum at a future date.
• You can use a present value calculation to
determine whether you'll receive more money by
taking a lump sum now or an annuity spread out
over a number of years.

6. Click to edit Master title style
6
Future Value (Accumulated value):
6
• The sum of all periodic payments along with the interest is
called the
future value (accumulated amount) of the annuity.
• The future value of an annuity is a way of calculating how
much money a series of payments will be worth at a certain
point in the future.
• By contrast, the present value of an annuity measures how
much money will be required to produce a series of future
payments.
• In an ordinary annuity, payments are made at the end of each
agreed-upon period. In an annuity due, payments are made at
the beginning of each period.

7. Click to edit Master title style
7
FORMULAE FOR PRESENT AND FUTURE VALUE
7

8. Click to edit Master title style
8 8
SAMPLE PROBLEMS

9. Click to edit Master title style
9
SAMPLE PROBLEMS
9

10. Click to edit Master title style
10
10
THANK YOU