Calculation of the Compound Growth Rate

Principle & Practice of Management

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Calculation of the Compound Growth Rate

Compound Growth Rate

Compound growth rate can be calculated with the following formula:
gr = Vo(1 + r)n = Vn
gr = Growth rate in percentage.
Vo = Variable for which the growth rate is needed (i.e., sales, revenue, the dividend at the end of year ‘0’).
Vn = Variable value (amount) at the end of year ‘n’.
(1 + r)n = Growth rate.

Doubling Period in Compound Growth Rate

The doubling period is the time required, to double the amount invested at a given rate of interest. For example, if you deposit Rs. 10,000 at 6 per cent interest, and it takes 12 years to double the amount. (See compound growth rate value for one rupee Table at 6 per cent till you find the closest value to 2).
The doubling period can be computed by adopting two rules, namely:
1. Rule of 72: To get doubling period 72 is divided by interest rate.
Doubling period (Dp) = 72 ¸ I
I = Interest rate.
Dp = Doubling period in years.
Illustration :
If you deposit Rs. 500 today at 10 per cent rate of interest, in how many years will this amount double?
Dp = 72 ¸ I = 72 ¸ 10 = 7.2 years (approx.)
2. Rule of 69: Rule of 72 may not give the exact doubling period, but the rule of 69 gives a more accurate doubling period. The
the formula to calculate the doubling period is:
Dp = 0.35 + 69 / I
Illustration :
Take the above problem as it is and calculate doubling period.
Dp = 0.35 + 69 / 10 = 7.25 years.

Compound Growth Rate

Effective Rate of Interest in Case of Doubling Period

Sometimes investors may have doubts as to what is the effective interest rate applicable if a financial institute pays the double amount at the end of a given number of years.
The effective rate of interest can be defined by using the following formula.
1. In case of rule of 72
ERI = 72 per cent Doubling period (Dp)
ERI = Effective rate of interest.
Dp = Doubling period.
2. In case of rule of 69
ERI = 69 + 0.35
Take the above example
ERI = 69 + 0.35
8 years
= 8.98 per cent or 9 per cent

Effective vs Nominal Rate

The nominal rate of interest or rate of interest per year is equal. Effective and nominal rate are equal only when the compounding is done yearly once, but there will be a difference, that is, the effective rate is greater than the nominal rate for shorter compounding periods. The effective rate of interest can be calculated with the following formula.
ERI ={( 1+ I/m)exponent m} – 1
I = Nominal rate of interest.
m = Frequency of compounding per year.

Sinking Fund Factor

The financial manager may need to estimate the number of annual payments so as to accumulate a predetermined amount after a future date, to purchase assets or to pay a liability. The following formula is useful to calculate the annual payment.
Ap = {FVAn[ I/(1+ I)exponent n]} – 1
Ap = Annual payment.
VAn = Future value after ‘n’ years.
I = Interest rate.