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Quantitative Aptitudeमात्रात्मक योग्यता · साधारण और चक्रवृद्धि ब्याज

Simple and Compound Interestसाधारण और चक्रवृद्धि ब्याज questions and answersप्रश्न और उत्तर

Interest questions reward pattern memory. Simple interest grows by the same amount every year; compound interest grows on the interest too. The difference between them follows a tiny formula.

  • Unlimitedअसीमित fresh questionsनए प्रश्न
  • Answersउत्तर always one tap awayहमेशा एक टैप दूर
  • 4 subtopicsउप-टॉपिक
  • SSC CGL ~1
  • IBPS PO ~1
  • TCS NQT ~1

Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।

How simple and compound interest worksसाधारण और चक्रवृद्धि ब्याज को समझिए

Simple interest is linear: the same interest every year, P × R / 100.

Compound interest multiplies: each year the amount becomes (1 + R/100) times the previous year. For 10% that is ×1.1, ×1.21, ×1.331.

The first year of CI and SI is identical. The gap appears from year 2 because CI earns interest on the first year’s interest.

Tricks that save timeसमय बचाने वाली ट्रिक्स

All tricks →सभी ट्रिक्स →

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Mental mathsमानसिक गणितRarely taughtकम सिखाई जाने वाली✓ Checked on 5 cases✓ 5 मामलों पर जाँची गई

Turn every % into a fraction multiplier, then cancel

Use it when:कब इस्तेमाल करें: Any chain of increases, decreases, discounts or taxes.

  1. Rewrite each change as a fraction: +20% → 6/5, −25% → 3/4, +12.5% → 9/8, −10% → 9/10.
  2. Multiply the fractions and cancel before computing anything.
Exampleउदाहरण

Marked 20% above cost, sold at 25% discount. Profit or loss?

→ 6/5 × 3/4 = 18/20 = 9/10 → 10% loss.

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Each percentage change multiplies the value by (1 ± r/100); a fraction is just that multiplier written exactly, and products of fractions cancel.

Limits:सीमाएँ: Best when the percentages are “fraction friendly” (multiples of 5, 12.5, 16.67, 33.33). For 17% or 23% use the decimal 1.17 / 0.77.

Formulaसूत्र✓ Checked on 150 cases✓ 150 मामलों पर जाँची गई

CI − SI for 2 and 3 years without computing either

Use it when:कब इस्तेमाल करें: The question gives (or asks for) the difference between compound and simple interest.

  1. 2 years: difference = P × (r/100)².
  2. 3 years: difference = P × (r/100)² × (3 + r/100).
Exampleउदाहरण

₹8,000 at 5% for 2 years: CI − SI?

→ 8,000 × 1/400 = ₹20

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Year 1 is identical. In year 2 CI also earns interest on year 1’s interest: P(r)(r). In year 3 it earns that twice more plus interest on interest-on-interest, giving P r² (3 + r).

Limits:सीमाएँ: Annual compounding only. For half-yearly, use r/2 and double the number of periods first.

Mental mathsमानसिक गणित✓ Checked on 51 cases✓ 51 मामलों पर जाँची गई

Rule of 72, 114 and 144 (double, triple, quadruple)

Use it when:कब इस्तेमाल करें: “In about how many years will money double (or triple) at r% compound interest?”

  1. Double: 72 ÷ r years. Triple: 114 ÷ r. Four times: 144 ÷ r.
  2. Exam options are usually whole years apart, so the estimate picks the answer.
Exampleउदाहरण

Double at 8% compound interest

→ 72 ÷ 8 = 9 years (exact: 9.01)

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Doubling time is ln 2 / ln(1 + r/100) ≈ 69.3/r for small r; 72 corrects for the curvature at typical exam rates of 6–12% and divides evenly by many numbers.

Limits:सीमाएँ: Doubling and tripling are within half a year, quadrupling within 0.7 years, for rates from 4% to 20%. For simple interest use 100 ÷ r for doubling instead.

Solved examplesहल किए गए उदाहरण

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

  1. Example 1उदाहरण 1 · Simple interest · Easyआसान

    Aarav deposits ₹4,500 in Bank of Baroda at 6% per annum simple interest. How much interest is earned in 4 years?

    1. ₹810
    2. ₹970
    3. ₹1,080
    4. ₹1,190
    Answer:उत्तर: ₹1,080
    1. SI = 4,500 × 6 × 4 / 100
    2. = ₹1,080.

  2. Example 2उदाहरण 2 · Compound interest · Easyआसान

    Rohan invests ₹20,000 at 8% per annum, compounded annually. Find the compound interest after 2 years.

    1. ₹2,995
    2. ₹3,328
    3. ₹3,661
    4. ₹3,994
    Answer:उत्तर: ₹3,328
    1. Year 1: 20,000 × 108/100 = ₹21,600.
    2. Year 2: 21,600 × 108/100 = ₹23,328.
    3. CI = 23,328 − 20,000 = ₹3,328.

  3. Example 3उदाहरण 3 · Difference between CI and SI · Easyआसान

    Find the difference between compound interest and simple interest on ₹1,500 at 10% per annum for 2 years.

    1. ₹14
    2. ₹15
    3. ₹17
    4. ₹18
    Answer:उत्तर: ₹15
    1. CI − SI = 1,500 × (10/100)²
    2. = 1,500 × 100/10000 = ₹15.

  4. Example 4उदाहरण 4 · Compound interest compounded half-yearly · Easyआसान

    Find the compound interest on ₹5,000 at 20% per annum for 1 year, interest compounded half-yearly.

    1. ₹1,000
    2. ₹1,050
    3. ₹1,075
    4. ₹6,050
    Answer:उत्तर: ₹1,050
    1. Rate per half-year = 20/2 = 10%; periods = 2.
    2. Amount = ₹5,000 × 1.1^2 = ₹6,050.
    3. CI = ₹6,050 − ₹5,000 = ₹1,050.

  5. Example 5उदाहरण 5 · Simple interest · Mediumमध्यम

    A sum of ₹14,500 lent by Tenzin becomes ₹18,850 in 4 years at simple interest. Find the rate of interest per annum (in %).

    1. 6 %
    2. 7.5 %
    3. 9 %
    4. 9.5 %
    Answer:उत्तर: 7.5 %
    1. SI = 18,850 − 14,500 = ₹4,350.
    2. R = 4,350 × 100 / (14,500 × 4) = 7.5%.

  6. Example 6उदाहरण 6 · Compound interest · Mediumमध्यम

    Fatima invests ₹6,000 at 20% per annum, compounded annually. Find the amount after 3 years.

    1. ₹8,294
    2. ₹9,331
    3. ₹10,368
    4. ₹12,442
    Answer:उत्तर: ₹10,368
    1. Year 1: 6,000 × 120/100 = ₹7,200.
    2. Year 2: 7,200 × 120/100 = ₹8,640.
    3. Year 3: 8,640 × 120/100 = ₹10,368.
    4. Amount = ₹10,368.

  7. Example 7उदाहरण 7 · Difference between CI and SI · Mediumमध्यम

    Find the difference between compound interest and simple interest on ₹12,500 at 4% per annum for 2 years.

    1. ₹10
    2. ₹15
    3. ₹20
    4. ₹25
    Answer:उत्तर: ₹20
    1. CI − SI = 12,500 × (4/100)²
    2. = 12,500 × 16/10000 = ₹20.

  8. Example 8उदाहरण 8 · Compound interest compounded half-yearly · Mediumमध्यम

    Find the compound interest on ₹18,000 at 20% per annum for 1 year, interest compounded half-yearly.

    1. ₹3,600
    2. ₹3,780
    3. ₹3,805
    4. ₹21,780
    Answer:उत्तर: ₹3,780
    1. Rate per half-year = 20/2 = 10%; periods = 2.
    2. Amount = ₹18,000 × 1.1^2 = ₹21,780.
    3. CI = ₹21,780 − ₹18,000 = ₹3,780.

Common mistakesआम गलतियाँ

  • Forgetting to subtract the principal when the question asks for interest, not amount.
  • Using the annual rate unchanged for half-yearly or quarterly compounding.
  • Rounding the multiplier (1.1³ = 1.331, not 1.33).

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न

What is the difference between simple and compound interest?

Simple interest is calculated only on the principal. Compound interest is calculated on the principal plus the interest already added.

What is the shortcut for CI − SI for 2 years?

Difference = P × (R/100)². For ₹10,000 at 10%, it is ₹100.

How do I handle half-yearly compounding?

Halve the rate and double the number of periods.

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