Page 39 - DMGT409Basic Financial Management

Basic Financial Management

Notes Illustration 1: ` 1,000 invested at 10% is compounded annually for three years, Calculate the
Compounded value after three years.
Solution:
Amount at the end of 1st year will be: 1,100

[1000 x 110/100 = 1,100]
Amount at the end of 2nd year will be: 1,210
[1100 x 110/100 = 1,210]
Amount at the end of 3rd year will be: 1,331
[1210 x 110/100 = 1,331]

This compounding process will continue for an indefinite time period.

Compounding of Interest over ‘N’ years: The compounding of Interest can be calculated by the
following equation.
A = P (1 + i) n

In which,
A = amount at the end of period ‘n’.
P = Principal at the beginning of the period.
I = Interest rate.

N = Number of years.
By taking into consideration, the above illustration we get,
A = P (1+i) n
A = 1000 (1 + .10) 3
A = 1,331

Note Computation by this formula can also become very time consuming if the number
of years increase, say 10, 20 or more. In such cases to save upon the computational efforts,
Compound Value table* can be used. The table gives the compound value of ` 1, after ‘n’
years for a wide range of combination of ‘I’ and ‘n’.
For instance, the above illustration gives the compound value of ` 1 at 10% p.a. at the end
of 3 years as 1.331, hence, the compound value of ` 1000 will amount to :
10001 × 331 = ` 1331

3.3.1 Multiple Compounding Periods

Interest can be compounded, even more than once a year. For calculating the multiple value
above, logic can be extended. For instance, in case of Semi-annual compounding, interest is paid
twice a year but at half the annual rate. Similarly in case of quarterly compounding, interest rate
effectively is 1/4th of the annual rate and there are four quarter years.

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