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18. Compound Interest, Zakat and Ushr

CSS GSA — Paper 7, Part-II, Section VI, Sub-topic 18 (Compound Interest, Zakat and Ushr)

Past Paper Weightage

  • High in Pakistan-context MPT/General Ability papers — Zakat and Ushr rate calculations are Pakistan-specific staples; compound interest is a standard financial-math question.

Simple Interest vs Compound Interest

  • Simple Interest (SI): interest calculated only on the original principal each period
SI=P×R×T100SI = \frac{P \times R \times T}{100}

where P=Principal, R=annual rate %, T=time in years

  • Compound Interest (CI): interest calculated on the principal PLUS all previously accumulated interest — grows faster than simple interest over time
  • Compound Interest formula:
A=P(1+R100)TA = P\left(1+\frac{R}{100}\right)^T CI=A−PCI = A - P

Worked Example 1 (Compound Interest)

  • Find the compound interest on Rs. 10,000 for 2 years at 10% per annum, compounded annually.
    • Step 1: Apply the formula
      • A=P(1+R/100)T=10,000×(1+10/100)2=10,000×(1.1)2.A = P(1+R/100)^T = 10,000 × (1+10/100)² = 10,000 × (1.1)².
    • Step 2: Calculate (1.1)² = 1.21, so A = 10,000 × 1.21 = Rs. 12,100.
    • Step 3: CI = A − P = 12,100 − 10,000 = Rs. 2,100.

Worked Example 2 (Compound Interest, Year-by-Year Check)

  • Verify the above using the year-by-year method.
    • Step 1: Year 1: Interest = 10,000 × 10/100 = Rs. 1,000. New principal = 10,000 + 1,000 = Rs. 11,000.
    • Step 2: Year 2: Interest = 11,000 × 10/100 = Rs. 1,100 (interest earned on the NEW, larger principal — this is what makes it "compound"). New total = 11,000 + 1,100 = Rs. 12,100.
    • Step 3: Total CI over 2 years = 1,000 + 1,100 = Rs. 2,100, confirming the formula result.

Zakat — Rate and Calculation

  • Zakat: an obligatory Islamic charitable contribution
Zakat=Wealth×0.025(2.5% per annum)\text{Zakat} = \text{Wealth} \times 0.025 \quad (2.5\% \text{ per annum})

levied on qualifying wealth/assets that have been held for one full lunar (Hijri) year and exceed the Nisab threshold (a minimum wealth level, traditionally based on the value of ~87.48 grams of gold or ~612.36 grams of silver)

  • Applies to: cash savings, gold/silver, tradeable business goods/inventory, and certain investments — held above Nisab for a full year

Worked Example (Zakat)

  • A person holds Rs. 500,000 in savings for over a year, above the Nisab threshold. Calculate the Zakat payable.
    • Step 1: Apply the Zakat rate: 2.5% of qualifying wealth.
    • Step 2: Calculate: 500,000 × 2.5/100 = 500,000 × 0.025.
    • Step 3: Zakat payable = Rs. 12,500.

Ushr — Rate and Calculation

  • Ushr: an Islamic agricultural levy on crop produce, distinct from Zakat
Ushr=Produce×{0.10(10%) natural irrigation0.05(5%) artificial irrigation\text{Ushr} = \text{Produce} \times \begin{cases} 0.10 & \text{(10\%) natural irrigation} \\ 0.05 & \text{(5\%) artificial irrigation} \end{cases}

on land irrigated by natural means (rainfall, rivers, springs — without extra cost/effort) the rate is 10%; on land irrigated using artificial/paid means (e.g., tube wells, purchased water, mechanical irrigation) the rate is 5% — the lower rate reflects the added cost/effort the farmer already bore

Worked Example (Ushr)

  • A farmer harvests 2,000 kg of wheat from rain-fed (naturally irrigated) land. Calculate the Ushr payable in kg.
    • Step 1: Since the land is naturally irrigated, the applicable rate is 10%.
    • Step 2: Calculate: 2,000 × 10/100 = 2,000 × 0.10.
    • Step 3: Ushr payable = 200 kg of wheat.

MCQ Traps

  • Zakat rate = 2.5%; Ushr on naturally-irrigated land = 10%; Ushr on artificially-irrigated land = 5% — these three rates are commonly swapped in MCQs, so memorize them as a set
  • Compound interest formula uses the exponent T on the WHOLE (1+R/100) term — don't multiply R/100 by T like in simple interest
  • Zakat applies to wealth held for a full lunar year above Nisab; Ushr applies to agricultural produce at harvest, with no "one year holding" requirement

Self-Test Questions

  1. Find the compound interest on Rs. 8,000 for 3 years at 5% per annum, showing the year-by-year breakdown.
  2. A person's qualifying savings are Rs. 640,000, held above Nisab for a full year. Calculate the Zakat payable, showing the formula.
  3. A farmer harvests 3,500 kg of rice from land irrigated by a tube well (artificial means). Calculate the Ushr payable.
  4. Compare the total interest earned on Rs. 20,000 at 8% per annum for 2 years under Simple Interest versus Compound Interest, showing both calculations.

Past-Paper MCQs (FPSC)

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The FPSC MCQ papers you shared (2024 and 2025) had no direct interest, Zakat or Ushr question.

Past-Paper Questions with Answers (FPSC)

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Every question below appeared in the FPSC papers you shared; the year and question number are in each title. Answers are worked out by me.

  • CSS 2021 Q7(d): Mr. Raheel invests Rs. 60,000 at simple interest; after 5 years it is worth Rs. 85,000. Find the yearly rate. (5)
    1. Interest earned = 85,000 − 60,000 = 25,000
    2. I = P × r × t ÷ 100 → 25,000 = 60,000 × r × 5 ÷ 100 = 3,000r
    3. r ≈ 8.33% per year
  • CSS 2020 Q8(d): Zahid left Rs. 1,750,000. His family pays a debt of Rs. 150,000; the rest goes to a son and a daughter, the son getting double. Find each share. (5)
    1. Net estate = 1,750,000 − 150,000 = 1,600,000
    2. Daughter = x, son = 2x → 3x = 1,600,000
    3. Daughter ≈ Rs. 533,333; son ≈ Rs. 1,066,667
  • CSS 2018 Q6(D): A man left property of Rs. 640,000; a debt of Rs. 40,000 was due to him and Rs. 5,000 was spent on his burial. Divide it among his widow, one daughter and two sons under Islamic law. (5)
    1. Reading 1 (the Rs. 40,000 is owed TO him, so it is added): estate = 640,000 + 40,000 − 5,000 = 675,000
    2. Widow gets 1/8 (children exist) = Rs. 84,375
    3. Remainder 590,625 is shared sons : daughter = 2 : 2 : 1 (5 parts of 118,125)
    4. Each son Rs. 236,250; daughter Rs. 118,125 (check: 84,375 + 472,500 + 118,125 = 675,000)
    5. Reading 2 (the Rs. 40,000 is a debt HE owed): estate = 640,000 − 40,000 − 5,000 = 595,000; widow 74,375; each son 208,250; daughter 104,125
    • Write which reading you take; the wording 'due to him' supports reading 1
  • CSS 2018 Q6(C): Profit sharing among partners who invest different amounts for different periods. (5)
    • Answered in the Ratios and Proportion chapter: multiply each investment by its months and share the profit in that ratio
  • CSS 2025 Q6(b): Deposit plus 36 equal instalments totalling 127% of the basic price. (5)
    • Answered in the Profit, Loss and Business Mathematics chapter: monthly payment ≈ Rs. 116,866.67

CSS Exam Perspective

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  • Most repeated areas: simple interest, Islamic inheritance (2018, 2020), partnership profit
  • Tip: for inheritance, first deduct debts and burial costs, then give the fixed shares (wife 1/8 with children), then split the rest 2:1 between sons and daughters