Comparison of Annual, Semi-annual and Quarterly Compounding
The effect of compounding more than once a year can also be expressed in the form of a formula. Equation 2.1 can be modified as Eq. 2.2.
in which m is the number of times per year compounding is made. For semi·annual compounding m would be 2, while for quarterly compounding it would equal 4 and if interest compounded monthly, weekly and daily, would equal 12, 52 and 365 respectively.
The general applicability of the formula can be shown as follows, assuming the same figures of Mr X’s savings of Rs 1,000
The table of the sum of Re 1 (Table A-1) can also be. used to simplify calculations when compounding occurs more than once a year. We are required simply to divide the interest rate by the number of times compounding occurs, that is (i + m) and multiply the years by the number of compounding periods per year, that is, (m x n). In our example, we have to look at Table A-1 for the sum of rupee one under the 3 per cent column and in the row for the fourth year when compounding is done semi-annually, the respective rate and year figures would be 1.5 per cent and the eighth year in quarterly compounding.
The compounding factor for 3 per cent and” years is 1.126 while the factor for 1.5 percent and 8 years is 1.127. Multiplying each of the factors by the initial savings deposit of Rs 1,000, we find Rs.l,126 (Rs 1,000 x 1.126) for semi-annual compounding and Rs 1,127 (Rs 1,000 x 1.127) for quarterly compounding. The corresponding values found by the long method are Rs 1,125.51 and Rs 1,126.49 respectively. The difference’ can be attributed to the rounding off of values in Table A-1.