Quantitative Aptitude — Formula Sheet
P3 · CA Foundation · Free and exam-ready
Ratio, Proportion, Indices & Logarithms
Full cheatsheet →Continued proportion (a, b, c)
a/b = b/c ⇒ b² = ac ⇒ b = √(ac)
n-th root via log
log ⁿ√x = (1/n) · log x
Ratio to percentage
a : b as % = a/(a+b) × 100
Time Value of Money
Full cheatsheet →Future value (compound)
FV = PV × (1 + r)^n
Present value
PV = FV ÷ (1 + r)^n
Ordinary annuity — FV
FV = PMT × [((1 + r)^n − 1) / r]
Ordinary annuity — PV
PV = PMT × [1 − (1 + r)^−n] / r
Annuity due — PV/FV
Multiply the ordinary-annuity value by (1 + r).
Perpetuity — PV
PV = PMT / r
EMI
EMI = P × r × (1 + r)^n / ((1 + r)^n − 1)
r = monthly rate (annual% ÷ 12 ÷ 100), n = number of months.
Measures of Central Tendency & Dispersion
Full cheatsheet →Mean (ungrouped)
x̄ = Σxi / n
Mean (grouped)
x̄ = Σ(fi · xi) / Σfi
Median (continuous)
Median = L + ((n/2 − cf) / f) × h
L = lower limit of median class, cf = cumulative freq before, f = freq of median class, h = class width.
Mode (continuous)
Mode = L + ((f1 − f0) / (2f1 − f0 − f2)) × h
f1 = freq of modal class, f0/f2 = freq of preceding/succeeding classes.
Variance
σ² = Σ(xi − x̄)² / n
Standard Deviation
σ = √[Σ(xi − x̄)² / n]
Coefficient of Variation
CV = (σ / x̄) × 100%