CA Foundation Quantitative Aptitude Formula Revision by Anurag Chauhan Sir

CA Foundation is scheduled for May 14, 16, 18, 20, 2026. Quantitative Aptitude is an important section, requiring not only understanding of concepts and thorough practice but also appropriate resources for last-minute revision. CA Foundation Quantitative Aptitude formula revision compilation will save your time, prevent last-minute stress, and improve retention. Read more to get the formula for the most important chapters.

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CA Foundation Mathematics of Finance

This section covers fundamental concepts and formulas in financial mathematics.

1. Simple Interest (SI)

• Formula for Simple Interest (SI): SI = P × R × T (R is rate in decimals).

• Formula for Amount (A): A = P + SI or A = P(1 + RT).

• Special Cases for Principal Multiples:

• To double Principal: R = 1/T or T = 1/R.

• To make Principal N times: R = (N - 1)/T or T = (N - 1)/R.

• Example: Finding Principal (P) and Rate (R)

• Problem: Amount after 4 years = ₹5800, Amount after 5 years = ₹6000.

• Solution Strategy: Annual SI = ₹200. P = ₹5000. Rate (R) = 4%.

2. Compound Interest (CI)

• Formula for Amount (A): A = P (1 + r/m)^(t*m), where m is compounding periods per year.

• Compounding Frequencies (m): Annually: 1, Semi-annually: 2, Quarterly: 4, Monthly: 12.

• Formula for Compound Interest (CI): CI = A - P or CI = P [ (1 + r/m)^(t*m) - 1 ].

• Difference (CI - SI):

• For 2 years: CI - SI = PR².

• For 3 years: CI - SI = PR²(R + 3).

• Depreciation: Scrap Value = Cost × (1 - Rate of Depreciation)^Time.

• Population Growth: Future Pop. = Initial Pop. × (1 + Rate of Growth)^Time.
  
  

Check, Also: CA Foundation Notes

3. Effective Rate of Interest

• Formula: (1 + r/m)^m - 1 (as a decimal).

• Example: Nominal Rate Misconception

• Problem: Nominal Rate = 2% per month, compounded monthly.

• Solution: Annual nominal rate = 24% p.a.. Effective Rate ≈ 26.82%.

4. Present Value (PV) of a Cash Flow

• Formula: PV = Future Value / (1 + r/m)^(t*m).

• Example:

• Problem: ₹5000 due after 4 years, market rate 6% p.a. semi-annually.

• Solution: PV ≈ ₹3947.

5. Annuities

• Definition: A series of equal payments at regular intervals.

• Types: Ordinary Annuity (payments at end), Annuity Due (payments at beginning).

• Components: n = t × m (Total payments), i = r / m (Interest rate per period).

• Future Value (FV) and Present Value (PV) Formulas:

• Application: FV for Investment, PV for Loan questions.

6. Perpetuity

• Definition: Annuity with infinite payments.

• Formulas:

• Regular Perpetuity (PV): PV = R / i.

• Immediate Perpetuity (PV): PV = R / i + R.

• Growing Perpetuity (PV): PV = R / (i - G) (G = rate of growth).

7. Sinking Fund

• Purpose: Provision for future financial obligation.

• Formula Used: Future Value of an Ordinary Annuity.

8. Net Present Value (NPV)

• Formula: NPV = PV of All Inflows - PV of All Outflows.

9. Leasing

• Concept: Calculates PV of Rent.

• Decision: Favorable for Owner if PV of Rent > Cost of Asset; for User if PV of Rent < Cost of Asset.

10. Valuation of Bond

• Concept: Determines fair price. Uses Coupon Rate and Investor's Expected Rate.

• Formula: Value = (PV of Interest Payments) + (PV of Maturity Amount).

• Example:

• Problem: Bond FV ₹2000, 3-year, 10% coupon. Investor expects 13% return.

• Solution: Value ≈ ₹1858.

11. Compound Annual Growth Rate (CAGR)

• Formula: CAGR = (Current Value / Base Value)^(1 / Difference of Time) - 1.

12. Real Rate of Return

• Formula: Real Rate = Nominal Rate - Inflation Rate.

13. Growth Rate in Population

• Example:

• Problem: Out of 1000 people, 52 deaths, 72 births. Double population in how many years?

• Solution: Net Growth Rate = 2%. Doubling time ≈ 35 years.

CA Foundation Maths - Central Tendency and Dispersion

This section covers measures used to describe the central position and spread of data.

1. Central Tendency - Introduction

• Purpose: To find the central location representing all observations.

• Types: THREE types: Mean, Median, Mode.

2. Arithmetic Mean (AM)

• Individual Series: Mean (X̄) = ΣX / N.

• Discrete/Continuous Series: Mean (X̄) = ΣfX / N.

• Shortcut Methods:

• Assumed Mean: X̄ = A + (ΣD / N) (D = X - A).

• Step-Deviation: X̄ = A + (ΣfU / N) × H (U = (X - A) / H).

• Important Properties:

• Σ(X - X̄) = 0.

• Sum of Absolute Deviations is MINIMUM from MEDIAN.

• Sum of Squared Deviations is MINIMUM from MEAN.

• Combined Mean: X̄_combined = (n1X̄1 + n2X̄2 + n3X̄3) / (n1 + n2 + n3).

• Characteristics:

• BEST measure.

• Highly AFFECTED by extreme items.

• NOT SUGGESTED for open-ended series.

3. Median

• Definition: The middle value in a sorted dataset, representing the central 50%.

• Calculation (Individual/Discrete Series):

• n odd: (n+1)/2 th rank.

• n even: Average of (n/2)th and (n/2 + 1)th terms.

• Calculation (Continuous Series): Median = L + [(N/2 - CF) / F] * H.

• L=Lower limit, N=Total obs., CF=Prev. Cum. Freq., F=Class Freq., H=Class width.

• Properties:

• Not affected by extreme values.

• Best for open-ended series.

• Calculated graphically using an Ogive.

4. Fractiles

• Definition: Values dividing data into specific equal parts.

• Quartiles: Divide data into four equal parts (Q1, Q2, Q3). Q2 is equivalent to the Median.

• Calculation (Individual/Discrete Series - Quartiles): Q1 = (n+1)/4 th term, Q3 = 3 * [(n+1)/4] th term.

• Calculation (Continuous Series - Quartiles):

• Q1 = L + [(N/4 - CF) / F] * H.

• Q3 = L + [(3N/4 - CF) / F] * H.

• (For continuous series, use N/4 (not N+1/4).).

• (Memory Tip: Quartiles divide by 4, Deciles by 10, Percentiles by 100.)

• Deciles: Divide series into 10 equal parts (D1 to D9). D5 is equivalent to the Median.

• Percentiles: Divide series into 100 equal parts (P1 to P99). (Memory Tip: P80 is equivalent to D8.)

• Comparison of Measures:

5. Mode

• Definition: The observation with the highest frequency.

• Calculation (Individual/Discrete Series): By inspection.

• Calculation (Continuous Series): Mode = L + [(F1 - F0) / (2F1 - F0 - F2)] * H.

• L=Lower limit of modal class, F1=Freq. of modal class, F0=Freq. of preceding class, F2=Freq. of succeeding class, H=Class width.

• Properties:

• Not affected by extreme observations.

• Calculated graphically using a Histogram.

6. Relationship Between Mean, Median, and Mode

• 3 Median = Mode + 2 Mean.

• (Mean - Mode) = 3 * (Mean - Median).

7. Impact of Change of Origin and Scale

• Mean, Median, and Mode are all affected by both Change of Origin and Change of Scale.

• Rule: For y = a + bx, New Measure(y) = a + b * Original Measure(x).

8. Geometric Mean (GM)

• Individual Series: GM = (x1 * x2 * … * xn)^(1/n).

• Applications: Used for the average of rates.

• Properties: GM(x * y) = GM(x) * GM(y); GM(x / y) = GM(x) / GM(y).

9. Harmonic Mean (HM)

• Individual Series: HM = n / Σ(1/x).

• Applications: Used for the average of rates, particularly average speed.

10. Relationships Among AM, GM, and HM

• Identical Observations: Mean = Median = Mode = GM = HM = K.

• Different Positive Observations: AM > GM > HM.

For two positive items 'a' and 'b': Arithmetic Mean * Harmonic Mean = (Geometric Mean)^2.