CA Foundation Paper 3 key terms

Interest calculated only on the original principal for the whole period, ignoring any interest already earned. Formula: SI = P × R × T ÷ 100, with T in years.

Interest computed on the principal plus previously accumulated interest, so the base grows each period. Amount = P(1 + i)^n, and compound interest equals that amount minus P.

The true annual growth rate actually produced when interest is compounded more than once a year. It equals (1 + i/m)^m − 1, where m is the number of compounding conversions per year.

The stated annual rate quoted before adjusting for how often compounding occurs. A nominal 12% compounded monthly does not grow a sum by 12% in a year, but by slightly more.

A series of equal payments made at regular intervals, such as a fixed monthly deposit. Payments may fall at each period end (ordinary annuity) or at each period start (annuity due).

The amount that must be invested today to produce a stated future sum, given a specified rate and time. It is found by discounting the future cash flow backwards.

The process of reducing a future amount to its equivalent value today by applying a rate of interest in reverse. It is the inverse operation of accumulating a sum forward.

An annuity whose equal payments continue forever with no end date. Its present value equals the periodic payment divided by the interest rate per period.

A fund built up through regular equal deposits so that a known future obligation can be met. The periodic deposit is found from the annuity formula rearranged for the payment.

An arrangement of selected items in which the order matters, so AB and BA count as different. The number of permutations of r items chosen from n distinct items is n! ÷ (n − r)!.

A selection of items in which order is irrelevant, so AB and BA count as the same choice. The count is n! ÷ [r!(n − r)!], often written nCr.

The product of all positive integers from 1 up to a given whole number, written with an exclamation mark. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120, and 0! is defined as 1.

If one task can be done in m ways and a second independent task in n ways, the two together can be done in m × n ways. It underpins most permutation and combination problems.

A sequence in which each term after the first is obtained by adding a fixed constant called the common difference. The nth term is a + (n − 1)d.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed constant ratio. The nth term is a·r^(n−1), and terms grow or shrink rapidly.

The total obtained by adding the first n terms of a series. For an arithmetic progression it is n/2 × (first term + last term); for a geometric progression a(r^n − 1)/(r − 1).

A well-defined collection of distinct objects treated as a single whole. Membership is decided by a clear rule, so any given object either belongs to the set or does not.

A set whose every element also belongs to another set. If A is a subset of B, then B contains at least all of A's elements, and every set is a subset of itself.

The set formed by combining all elements appearing in either set, with duplicates counted once. It is written A ∪ B and read as A union B.

The set of elements common to both sets, written A ∩ B. If the two sets share nothing, their intersection is the empty set.

A diagram using overlapping circles inside a rectangle to show sets and their relationships. Overlaps represent intersections, and the surrounding rectangle usually represents the universal set.

A declarative statement that is either definitely true or definitely false, but not both. Questions and commands are not propositions because no truth value can be assigned.

The opposite of a statement, formed by inserting or removing 'not' so that the truth value reverses. If a proposition is true, its negation is false, and conversely.

A compound statement joining two propositions with 'and', written p ∧ q. It is true only when both component statements are true, and false otherwise.

A compound statement joining two propositions with 'or', written p ∨ q. It is false only when both components are false, and true in every other case.

A table listing every possible combination of truth values for the components of a compound statement and the resulting value of the whole. It tests validity exhaustively.

The arithmetic average, found by adding all observations and dividing by their number. It uses every value, so extreme observations can pull it sharply away from the typical value.

The middle value of observations arranged in order; with an even count it is the average of the two central values. Unlike the mean, it is barely affected by extreme outliers.

The value that occurs most frequently in a data set. A distribution may have no mode, one mode, or several modes, and it applies to qualitative data as well as numbers.

The positive square root of the variance, expressing how far observations typically lie from the mean in the original units. A larger value indicates greater dispersion.

The average of the squared deviations of observations from their mean. Squaring removes signs but changes units, so variance is expressed in squared units of the data.

The standard deviation expressed as a percentage of the mean, giving a unit-free measure of relative variability. It allows consistency to be compared across data sets with different units or levels.

One of three values dividing ordered data into four equal parts: the lower quartile, the median, and the upper quartile. The middle half of the data lies between the outer two.

The difference between the largest and smallest observations in a data set. It is quick to compute but depends only on the two extreme values and ignores everything between them.

A numerical measure of the strength and direction of a linear relationship between two variables, ranging from −1 to +1. A value near zero means little linear association.

A method of fitting an equation that predicts one variable from another by minimising squared deviations. The regression line passes through the means of both variables.

A graph plotting one variable on each axis so that each observation appears as a point. The pattern of points reveals whether a relationship is positive, negative, or absent.

A single figure expressing the change in a variable or group of variables relative to a chosen base period, which is set at 100. It simplifies comparison of values over time.

The reference period against which index numbers for other periods are compared, assigned an index value of 100. Its choice strongly affects how changes are interpreted.