InvestorQ : Does frequency of compounding also impact my present value of future cash flows? # Does frequency of compounding also impact my present value of future cash flows? Answer 1 year ago

Compounding refers to the frequency with which interest rates are charged or paid during a given year. In practice, interest rates can be compounded anywhere from once per year to once per day; the theoretical limiting case is known as continuous compounding, in which rates are compounded at every instant in time. Compounding frequency is one of the most important determinants of the future value and the present value of a sum. Here is how it works in practice.

For example, if a bank offers a 4% rate of interest with annual compounding, an investor who holds Rs.1,000 in the bank for one year will have a balance of: Rs.1,000(1 + 0.04) = Rs.1,040 at the end of the year. In other words, the future value of this sum is Rs.1,040 at the end of 1 year.

If the interest is compounded semi-annually, then the investor will receive half of the annual rate twice per year; i.e., 2% every six months during the year. At the end of six months, the investor will have a balance of: Rs.1,000(1 + 0.02) = Rs.1,020 at the end of the year, the investor will have a balance of: Rs.1,020(1 + 0.02) = Rs.1,000(1 + 0.02)(1 + 0.02) = Rs.1,000(1 + 0.02)2 = Rs.1,040.40. In this case, since the principal is Rs.1,000, the total interest is Rs.40.40. Of this: Rs.40 is simple interest (interest on principal) Rs.0.40 is compound interest (interest on interest). This is fundamental to the power of compounding which is the core of systematic investment plans.

In the above case, the investor received an interest payment of Rs.1,000 (0.02) = Rs.20 at the end of six months, for a balance of Rs.1,020. The interest payment at the end of the year was based on the principal (Rs.1,000) and the interest (Rs.20) in the account. The interest paid on the principal was Rs.1,000(0.02) = Rs.20 and the interest paid on the interest was Rs.20(0.02) = Rs.0.40. Combined with the Rs.20 interest paid at the end of six months, the total interest paid during the year was Rs.20 + Rs.20 + Rs.0.40 = Rs.40.40. Of this, the Rs.40 was based on the principal; this is the simple interest. The remaining Rs.0.40 was based on the interest earned during the year; this is the compound interest. This basically goes to show why the frequency of compounding is important. That is because the compounding is all about interest on interest and makes compounding really work in your favour.

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