Page 41 - DMGT409Basic Financial Management

Basic Financial Management

Notes 3.3.3 Compound Sum of an Annuity

An annuity is a stream of equal annual cash flows. Annuities involve calculations based upon the

regular periodic contribution or receipt of a fixed sum of money.
Example: Mr Ramesh deposits ` 2,000 at the end of every year for 5 years in his saving
account, paying 5% interest compounded annually. Determine the sum of money, he will have at
the end of the 5th year.
Solution:

End of Year Amount Number of Compounded Interest Future Sum
Deposited Years compounded factor From Table 3
1 2 3 4 5
1 ` 2,000 4 1.216 ` 2,432
2 2,000 3 1.158 2,316
3 2,000 2 1.103 2,206
4 2,000 1 1.050 2,100
5 2,000 0 1.000 2,000
Amount at the end of 5th Year ` 11,054
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. They are given in Table A – 2. 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 ` 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 `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.

Example: 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 (i.e. Table A – 2) gives the compound value as 3,215, when `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

34 LOVELY PROFESSIONAL UNIVERSITY