Page 27 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Personal Financial Planning

Notes Finding the common factor of ` 2,000
= ` 2,000 (1.216+1.158+1.103+1.050+1.000)
= ` 2,000(5.527)
= ` 11,054

The above illustration depicts that in order to find the sum of the annuity, the annual amount
must be multiplied by the sum of the appropriate compound interest factors. Such calculations
are available for a wide range of I and n. To find the answer to the annuity question of illustration
3 we are required to look for the 5% column and the row for the five years and multiply the
factor y annuity amount of ` 2000. From the table we find that the sum of annuity of Re. 1
deposited at the of each year for 5 years is 5.526(IF). Thus, when multiplied by ` 2,000 annuity (A)
we find the total sum as ` 11,052.
Symbolically S = IF × A
n
Where,
A = is the value of annuity.

IF = represents the appropriate factor for the sum of the annuity of Re.1.
S = represents the compound sum of annuity.
n
Annuity tables are great innovations in the field of investment banking as they guide the
depositors and investors as to what sum amount (X) paid for number of years, n, will accumulate
to, at a stated rate of compound interest.
Illustration 5

Find the compound value of annuity, when three equal yearly payments of ` 25,000 are deposited
into an account, that yields 7% compound interest.
Solution:

The Annuity Table gives the compound value as 3,215, when Re.1 is paid every year for 3 years
at 7%. Thus, the compounded value of annuity of ` 2,000 is :
S = IF × A
n
S = 3.215 × 2000
n
S = 6,430
n
2.4 Discounting or Present Value Concept

The concept of present value is the exact opposite of that of a sum of money or series of payments,
while in case of present value concept, we estimate the present worth or a future payment/
installment or series of payment adjusted for the time value of money.
The basis of present value approach is that, the opportunity cost exist for money lying idle. That
is to say, that interest can be earned on the money. This return is termed as ‘discounting rate’.

!

Caution Given a positive rate of interest, the present value of the future Rupee will always
be lower. The technique for finding the present value is termed as ‘discounting’.

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