MB Applied Math 40S key terms

Interest computed each period on the original principal plus all interest already earned, so the balance grows by a constant multiplier rather than a constant amount.

The original amount of money borrowed or invested, before any interest is added or any payments are made.

The stated yearly interest rate before adjusting for how often compounding occurs; it must be divided by the number of compounding periods per year for calculations.

The true yearly growth rate after compounding is taken into account; it lets you compare investments or loans that compound at different frequencies on equal footing.

The interval of time between successive additions of interest to a balance, such as monthly, quarterly, or annually.

The amount an investment or debt will be worth at a specified later date after interest has been applied over the full term.

The amount of money today that would grow into a given future amount at a stated rate; it is the future value discounted back to the present.

The process of reducing a future amount to its equivalent value today by removing the interest it would have earned.

A series of equal payments made at regular intervals over a fixed time span, such as monthly loan payments or retirement contributions.

A series of equal regular payments in which each payment is made at the end of its period rather than at the beginning.

A series of equal regular payments in which each payment is made at the beginning of its period, so every payment earns interest for one extra period.

The gradual paying off of a debt through scheduled payments, where each payment covers interest owed plus some reduction of the outstanding balance.

A table listing each payment on a loan, showing how much goes to interest, how much reduces the principal, and the remaining balance.

The amount of principal still owed on a loan after a given number of payments have been made.

Interest calculated only on the original principal for the whole term, never on previously earned interest.

Two or more events that cannot occur at the same time in a single trial, so the probability of both happening together is zero.

Events where the occurrence of one does not change the probability of the other, so their joint probability equals the product of their separate probabilities.

Events where the outcome of one affects the probability of the other, as when items are drawn without replacement.

The probability that an event occurs given that another event is already known to have happened, written as P(A given B).

A formula for the probability that at least one of two events happens; it adds their probabilities and subtracts the probability of both.

A formula for the probability that two events both happen, obtained by multiplying the probability of the first by the conditional probability of the second.

The set of all outcomes in the sample space that are not in a given event; its probability equals one minus the event's probability.

The complete list or set of every possible outcome of a probability experiment.

A table, graph, or formula that assigns a probability to each possible value of a random variable, with all probabilities summing to one.

The long-run average outcome of a random variable, found by multiplying each value by its probability and adding the products.

A measure of how spread out values are around the mean, equal to the square root of the variance.

A symmetric bell-shaped probability curve described by its mean and standard deviation, used to model many real-world measurements.

The number of standard deviations a value lies above or below the mean, computed as the difference from the mean divided by the standard deviation.

An arrangement of items in which the order matters, such as the possible finishing orders of racers.

A selection of items from a larger group in which the order of selection does not matter, such as choosing a committee.

The product of all positive whole numbers from one up to a given number, written with an exclamation mark and used in counting formulas.

A rule that assigns exactly one output value to each input value in its domain.

The domain is the set of all allowed input values of a function; the range is the set of all output values it actually produces.

A function that undoes another function, sending each output back to the input that produced it; it exists only when the original is one-to-one.

A function in which the variable appears in the exponent, producing growth or decay by a constant factor over equal intervals.

The exponent to which a base must be raised to produce a given number; it is the inverse operation of exponentiation.

A pattern in which a quantity changes by a fixed percentage each period, increasing or decreasing ever faster in absolute size.

The time required for a decaying quantity to fall to half of its starting amount, used in radioactive decay and similar models.

A function whose values repeat at regular intervals, such as sine and cosine, making it useful for modelling cycles.

Half the distance between the maximum and minimum values of a periodic graph, measuring how far it swings from its centre line.

The length of the smallest interval over which a periodic function completes one full cycle and begins repeating.

An angle measure defined by arc length on a circle; one radian is the angle subtended by an arc equal in length to the radius.

A relationship stating that in any triangle, each side divided by the sine of its opposite angle gives the same value.

A relationship generalizing the Pythagorean theorem to any triangle, relating one side to the other two sides and the angle between them.

The situation when using the sine law with two given sides and a non-included angle may yield zero, one, or two valid triangles.

The distance measured along a curved portion of a circle, calculated from the radius and the central angle in radians.

The area of the pie-shaped region of a circle bounded by two radii and the arc between them.

The total area of all outer faces or curved surfaces of a three-dimensional object, measured in square units.

The amount of three-dimensional space an object occupies, measured in cubic units.

A three-dimensional figure made by combining two or more simpler solids, whose measurements are found by adding or subtracting the parts.

The ratio comparing corresponding lengths of a figure and its enlarged or reduced image; areas and volumes change by its square and cube.

Shapes with identical angles and proportional side lengths, so one is a scaled copy of the other.