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In accounting, the principal is the original amount borrowed or lent on which interest is then paid or given.The word "principal" is also used in many areas of mathematics to denote one particular object chosen from many possible ones. For example, the principal value of a multivalued function is the canonical value chosen to associate with that functions for convenient or by convention, e.g., 1 for (even though ).

The Sharpe ratio is a risk-adjusted financial measure developed by Nobel Laureate William Sharpe. It uses a fund's standard deviation and excess return to determine the reward per unit of risk. The higher a fund's Sharpe ratio, the better the fund's "risk-adjusted" performance, given bywhere is the return on the portfolio, is the risk-free return and is the standard deviation of the fund's returns (i.e., the portfolio risk).

Let be the principal (initial investment), be the annual compounded rate, the "nominal rate," be the number of times interest is compounded per year (i.e., the year is divided into conversion periods), and be the number of years (the "term"). The interest rate per conversion period is then(1)If interest is compounded times at an annual rate of (where, for example, 10% corresponds to ), then the effective rate over the time (what an investor would earn if he did not redeposit his interest after each compounding) is(2)The total amount of holdings after a time when interest is re-invested is then(3)Note that even if interest is compounded continuously, the return is still finite since(4)where e is the base of the naturallogarithm.The time required for a given principal to double (assuming conversion period) is given by solving(5)or(6)where ln is the natural logarithm. This function can be approximated by the so-called..

The simple first-order difference equation(1)where(2)(3)and(4)(5)are the price-demand and price-supply curves, where and represent the slope and -intercept, respectively, for the demand curve, and and represent the corresponding constants for the supply curve (Ezekiel 1938, Goldberg 1986).A class of behaviors related to this equation is known as "Cobweb phenomena" in economics.

Actuarial science is the study of risk through the use of mathematics, probability, and statistics. A person who performs risk assessment is known as an actuary. Actuaries typically are employed in financial, insurance, pensions, and other related sectors.Actuarial science is similar to medicine in that a lot of time must be taken for schooling and taking examinations, but salaries are typically rather high.The Season 1 episode "Sacrifice" (2005) of the television crime drama NUMB3RS mentions actuarial science.

Interest which is paid only on the principal and not on the additional amount generated by previous interest payments. A formula for computing simple interest iswhere is the sum of principal and interest at time for a constant interest rate .

The time required for a given principal to double (assuming conversion period) for compound interest is given by solving(1)or(2)where ln is the natural logarithm.This function can be approximated by the so-called "rule of 72":(3)The above plots show the actual doubling time (left plot) and the difference between the actual doubling time and the doubling time calculated using the rule of 72 (right plot) as a function of the interest rate .

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