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Annual Compounding

Table 2.1

Annual Compounding

This compounding procedure will continue for an indefinite number of years. The compounding of interest can be calculated by the following equation:

Thus, after substitution the actual figures' for the investment of Rs 1,000 in the formula A = P (1 + 1l), we arrive at the same result as in Table 2.1. This is the fundamental equation of . compound interest. The formula is useful as it can be applied quite readily for wide ranges of i and ii. However, the calculations involved will be tedious and time-consuming if the number of
years involved is large, say, 15 years or 20 years, To find the compound value of Rs 1,000, assuming the rate of interest to be 5 per cent, the compounding factor 1.05 is to be raised to. fifteenth power or twentieth power. In order to simplify, the compound interest' calculations, compound interest tables for values (1 + 1) for wide ranges of i and n have been compiled, Table A-1 given in Appendix 1 at the end of the book gives compound value. interest factor of one rupee at different rates of interest for different time periods, The compounded values can be readily calculated with the help of Table A-1. For instance, if Mr X wishes to find out how much his savings, will accumulate to in 15 years at 5 per cent rate of interest, application of the formula will require solving 1.05 raised to the power of fifteen: Rs 1,000 (1.05)is = A

Using Table A·1, we find that the compound value interest factor of Rs 1 at ; percent interest rate for 1 years is 2,079. Multiplying the initial principal (Rs 1, by 2.079, we obtain Rs 2,079. Which the help of the table, it is possible to calculate the compounded value for any combination of interest rate, i and number of years, Let us take another illustration.

The' tom pound interest phenomenon is most commonly associated with various savings institutions. These institutions emphasis the fact that they pay compound interest on savings deposited with them. If an investor deposits Rs 20,000 with a bank which is paying interest at 8 per cent on a 15 year time deposit, we consult Table A-1 and read the relevant value in the 15th .row (time period) in-the column of 8 per cent (rate of interest). This value is 3.172. Multiplying this factor by the actual deposit of Rs 20,000, we find his savings will accumulate to Rs 63,440.

Two important observations can be made from the Table A-1 for the sum of Re one. The first is that as the interest rate increases for any given year, the compound interest factor also increases. Thus, the higher the interest rate, the greater is the future sum. The second point is that for a given interest rate, the future sum of a rupee increases with the passage of time: Thus, the longer the period of time, the higher is the compound interest factor. However, it should be come in mind that for an interest rate of zero per cent, the compound interest factor always equals 1 and, therefore, the future amount always equals the initial principal: