CA Foundation Paper 3 flashcards

36 cards. Read the term and the definition here. The deck at the top of this page is optional.

Simple interest formula

SI = P × r × t / 100, where P is principal, r is the annual rate in percent, and t is time in years. The amount is P + SI.

Compound amount formula

A = P(1 + r/100)^n for annual compounding. Here r is the annual rate in percent, n is the number of years, and P is the principal invested.

Effective annual rate

EAR = (1 + r/(100m))^m − 1 when nominal rate r is compounded m times per year. It converts a nominal rate into an equivalent annual rate.

Annuity present value

PV = A × [1 − (1 + i)^(−n)] / i for an ordinary annuity of A per period at rate i per period over n periods. For annuity-due multiply by (1 + i).

Combination formula

nCr = n! / [r!(n − r)!] gives the number of ways to choose r items from n without regard to order. Note that nCr = nC(n−r).

Permutation formula

nPr = n! / (n − r)! counts ordered arrangements of r items chosen from n distinct items. Order matters, unlike combinations where it does not.

Logarithm product rule

log(ab) = log a + log b for positive a and b. Related rules are log(a/b) = log a − log b and log(a^k) = k log a.

Straight line slope

For y = mx + c, slope m = (y2 − y1)/(x2 − x1). Two lines are perpendicular when m1 × m2 = −1 and parallel when their slopes are equal.

Present value single sum

PV = FV / (1 + i)^n discounts a future amount FV back n periods at rate i per period. The discount factor falls as i or n rises.

Sinking fund deposit

A = FV × i / [(1 + i)^n − 1] is the periodic deposit needed to accumulate FV after n periods at rate i per period.

Banker's gain

Banker's gain = Banker's discount − True discount. Banker's discount is computed on the amount, while true discount is computed on the present value.

Determinant of 2×2 matrix

For matrix [[a,b],[c,d]], determinant = ad − bc. A zero determinant means the matrix is singular and has no inverse.

Union of two sets

n(A ∪ B) = n(A) + n(B) − n(A ∩ B). For three sets, subtract pairwise intersections and add back the triple intersection to avoid double counting.

Perpetuity present value

PV = A / i gives the present value of a level payment A received at the end of every period forever, discounted at rate i per period.

Number series difference rule

Compute successive differences; constant differences indicate an arithmetic series, while constant ratios indicate a geometric series. Check second differences for quadratic patterns.

Syllogism validity rule

A conclusion follows only if it holds in every Venn diagram consistent with the premises. A possibility conclusion fails if any one counter-diagram exists.

Clock hand angle

Angle between hour and minute hands = |30H − 5.5M| degrees, where H is the hour and M the minutes. The hands coincide 11 times in 12 hours.

Calendar odd days

A normal year shifts the weekday by 1 and a leap year by 2. In 100, 200, 300, and 400 years the odd days are 5, 3, 1, and 0 respectively.

Ranking total count

If a person is Lth from the left and Rth from the right in a row, total people = L + R − 1. This avoids double-counting the person.

Circular arrangement count

n distinct people can be seated around a circle in (n − 1)! distinct clockwise orders, because rotations of the same order are identical.

Direction sense displacement

Track movement with signed coordinates; final distance = √(x² + y²) and final direction follows the signs of the net x and y displacements.

Statement assumption test

An assumption is what the speaker takes for granted. Reject options that merely restate the statement or introduce conditions unrelated to it.

Strong argument test

A strong argument is relevant to the statement, substantial in impact, and follows logically. Weak arguments are trivial, emotional, or ambiguous.

Course of action validity

A valid course of action must be practical, directly address the problem in the statement, and stay within the authority implied by it.

Data sufficiency approach

Decide whether the given data is sufficient to answer the question, not what the numerical answer is. Evaluate each statement independently unless stated otherwise.

Grouped data mean

For grouped data, x̄ = Σfx / Σf, where x is each class midpoint and f its frequency. For raw data, x̄ = Σx / n.

Grouped data median

M = L + [(N/2 − cf)/f] × h, where L is the lower boundary of the median class, cf the cumulative frequency before it, f its frequency, and h the class width.

Grouped data mode

Mo = L + [(f1 − f0)/(2f1 − f0 − f2)] × h, where f1 is the modal class frequency and f0, f2 are the adjacent class frequencies.

Coefficient of variation

CV = (σ / x̄) × 100 expresses standard deviation as a percentage of the mean. It compares variability across data sets with different units or means.

Combined mean

For two groups, combined mean = (n1x̄1 + n2x̄2) / (n1 + n2). It weights each group mean by its size, not by taking a simple average.

Correlation coefficient range

The correlation coefficient r lies between −1 and 1. Values near ±1 indicate strong linear association; r = 0 indicates no linear correlation.

Addition rule probability

P(A or B) = P(A) + P(B) − P(A and B). For independent events, P(A and B) = P(A) × P(B), and P(A|B) = P(A and B)/P(B).

Binomial distribution

P(X = r) = nCr p^r q^(n−r) for n independent trials with success probability p and q = 1 − p. Mean = np and variance = npq.

Normal distribution rule

The normal curve is symmetric about its mean. About 68% of values lie within 1σ, 95% within 2σ, and 99.7% within 3σ of the mean.

Fisher's ideal index

Fisher's ideal index is the geometric mean of the Laspeyres and Paasche indices. Laspeyres uses base-year quantities; Paasche uses current-year quantities.

Pearson skewness

Karl Pearson's skewness = (mean − mode)/σ, or 3(mean − median)/σ. A positive value means a longer right tail; zero means symmetry.