Actuarial notation

Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. Traditional notation uses a halo system, where symbols are placed as superscript or subscript before or after the main letter. Example notation using the halo system can be seen below. Various proposals have been made to adopt a linear system, where all the notation would be on a single line without the use of superscripts or subscripts. Such a method would be useful for computing where representation of the halo system can be extremely difficult. However, a standard linear system has yet to emerge. is the annual effective interest rate, which is the "true" rate of interest over a year. Thus if the annual interest rate is 12% then . (pronounced "i upper m") is the nominal interest rate convertible times a year, and is numerically equal to times the effective rate of interest over one th of a year. For example, is the nominal rate of interest convertible semiannually. If the effective annual rate of interest is 12%, then represents the effective interest rate every six months. Since , we have and hence . The "(m)" appearing in the symbol is not an "exponent." It merely represents the number of interest conversions, or compounding times, per year. Semi-annual compounding, (or converting interest every six months), is frequently used in valuing bonds (see also fixed income securities) and similar monetary financial liability instruments, whereas home mortgages frequently convert interest monthly. Following the above example again where , we have since . Effective and nominal rates of interest are not the same because interest paid in earlier measurement periods "earns" interest in later measurement periods; this is called compound interest. That is, nominal rates of interest credit interest to an investor, (alternatively charge, or debit, interest to a debtor), more frequently than do effective rates. The result is more frequent compounding of interest income to the investor, (or interest expense to the debtor), when nominal rates are used.