Compound interest means that, the interest will include interest calculated on interest. The interest accrued on a principal amount is added back to the principal sum, and the whole amount is then treated as new principal, for the calculation of the interest for the next period.
For example, if an amount of Rs. 5,000 is invested for two years and the sinterest rate is 10%, compounded yearly:
* At the end of first year the interest would be (Rs. 5,000*0.10) or Rs.500
* In the second year the interest rate of 10% will applied not only to Rs. 5000but also to the Rs. 500 interest of the first year.
Thus in the second year the interest would be (0.10*Rs. 5500) or Rs. 550
For any loan or borrowing unless simple interest is stated, one should always assume interest is compounded. When compound interest is used we must always know how often the interest rate is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new principal, i.e. (interest + principal). The first term we must understand in dealing with compound interest is conversion period. Conversion period refers to how often the interest is calculated over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per year would be two. If the loan or deposit was for five years, then the number of conversion periods would be ten. Formula for calculating Compound Interest:
C = P (1+i)n
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5%
compounded quarterly
P = Rs. 10,000
i = 0.075 / 4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is:
C = Rs. 10,000(1 + 0.01875)^20
= Rs 10,000 x 1.449948
= Rs 14,499.48
So at the end of five years Mr. X would earn Rs. 4,499.48 (Rs.14,499.48 – Rs.10,000) as interest. This is also called as Compounding. Compounding plays a very important role in investment since earning a simple interest and earning an interest on interest makes the amount received at the end of the period for the two cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple interest option, then the amount that he would earn is calculated by applying the following formula:
S = P (1 + rt),
P = 10,000
r = 0.075
t = 5
Thus, S = Rs. 10,000[1+0.075(5)]
= Rs. 13,750
Here, the simple interest earned is Rs. 3,750. A comparison of the interest amounts calculated under both the method indicates that Mr. X would have earned Rs. 749.48 (Rs.4,499.48 – Rs. 3,750) or nearly 20% more under the compound interest method than under the simple interest method.
Simply put, compounding refers to the re-investment of income at the same rate of return to constantly grow the principal amount, year after year. Should one care too much whether the rate of return is 5% or 15%? The fact is that with compounding, the higher the rate of return, more is the income which keeps getting added back to the principal regularly generating higher rates of return year after year.
The table below shows you how a single investment of Rs 10,000 will grow at various rates of return with compounding. 5% is what you might get by leaving your money in a savings bank account, 10% is typically the rate of return you could expect from a one-year company fixed deposit, 15% – 20% or more is what you might get if you prudently invest in mutual funds or equity shares.
The Impact of Power of Compounding: The impact of the power of compounding with different rates of return and
different time periods:
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