Frequency of Compounding

In time value of money, in addition to base interest rate, the frequency with which interest is compounded also has an important bearing on the total interest charges associated with an instrument. The frequency of compounding is denoted by the standard formula of (1 + i)".  For example, a carrying charge of 1.0  percent per month compounded monthly will be equal to an annual interest rate of (1.01)12, i.e. 12.7 percent. Similarly, a 1.5 percent monthly rate is equivalent to 19.7% once annually. The more the frequent interest is compounded within the same year, the annual rate will be higher and higher. Compounding on a daily basis will have the highest annualized compound rate of interest for the same simple interest rate. 

You may notice that the expression (1 + i) appears in all six of the basic interest formulae. If the total elapsed time is held constant (normally 1 year) and the compounding period is reduced (or in the other way the frequency of compounding is increased, the value of this expression will also increase. The compounding frequency may be the deciding factor in choosing an investment from alternatives all of which has the same return. For example, in case of all investments having 6.0 percent annually, the effective rates may vary depending upon compounding frequency. The effective interest rate on money compounded annually is 6.00 percent. Semi-annually 6.09 percent, quarterly 6.14 percent, bimonthly  6.15 percent, monthly 6.18 percent  and continuously 6.1 9 percent.