Читать книгу Fundamentals of Financial Instruments - Sunil K. Parameswaran - Страница 72

Before analyzing interest computation techniques, let us first define certain key terms.

 Measurement Period: The unit in which time is measured for the purpose of stating the rate of interest is called the measurement period. The most common measurement period is one year, and we will use a year as the unit of measurement unless otherwise specified. That is, we will typically state that the interest rate is x%, say 10%, where the implication is that the rate of interest is 10% per annum.

 Interest Conversion Period: The unit of time over which interest is paid once and is reinvested to earn additional interest is referred to as the interest conversion period. The interest conversion period will typically be less than or equal to the measurement period. For instance, the measurement period may be a year, whereas the interest conversion period may be three months. Thus, interest is compounded every quarter in this case.

 Nominal Rate of Interest: The quoted rate of interest per measurement period is called the nominal rate of interest. For instance, in Example 2.1 the nominal rate of interest is 10%.

 Effective Rate of Interest: The effective rate may be defined as the interest that a dollar invested at the beginning of a measurement period would have earned by the end of the period. Quite obviously the effective rate will be equal to the quoted or nominal rate if the length of the interest conversion period is the same as that of the measurement period, which means that interest is compounded only once per measurement period. However, if the interest conversion period is shorter than the measurement period – or in other words, if interest is compounded more than once per measurement period – then the effective rate will exceed the nominal rate of interest. Take the case where the nominal rate is 10% per annum. If interest is compounded only once per annum, an initial investment of $1 will yield $1.10 at the end of the year, and we would say that the effective rate of interest is 10% per annum. However, if the nominal rate is 10% per annum, but interest is credited every quarter, then the terminal value of an investment of one dollar will definitely be more than $1.10. The relationship between the effective rate and the nominal rate will be derived subsequently. It must be remembered that the term nominal rate of interest is being used in a different context than in the earlier discussion where it was used in the context of the real rate of interest. The potential for confusion is understandable yet unavoidable.