Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए। A man invested Rs P at 10 % p.a. on simple interest for two years. Quantity I : if at the end of second year he gets Rs . 300 as interest, then find P Quantity II : Rs 3000 एक आदमी ने P रुपये 10% प्रति वर्ष के साधारण ब्याज पर दो साल के लिए निवेश किया। मात्रा I : यदि दूसरे वर्ष के अंत में उसे रु. 300 ब्याज के रूप में मिला , तो P ज्ञात कीजिए मात्रा II: 3000 रुपये

  1. Quantity : I > Quantity : II मात्रा : I > मात्रा : II

  2. Quantity : I ≥ Quantity : II मात्रा : I ≥ मात्रा : II

  3. Quantity : I < Quantity : II मात्रा : I < मात्रा : II

  4. Quantity : II ≥ Quantity : I मात्रा : II ≥ मात्रा : I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest for 2 years at 10% = 20% of P. Given interest = 300, so 20% of P = 300, therefore P = 300/0.2 = 1500. Comparing Quantity I (1500) with Quantity II (3000): 1500 < 3000, so Quantity I < Quantity II.

Multiple choice

Find the correct relationship between given quantities. Q1: Two equal amounts are invested for 2 years at 9% per annum by Anushika, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 100, then what is the amount? Q2: Two equal amounts are invested for 2 years at 11% per annum by Anushika, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 97, then what is the amount?

  1. Q1 > Q2

  2. Q1 ≥ Q2

  3. Q1 < Q2

  4. Q1 ≤ Q2

  5. Q1 = Q2 or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For CI-SI difference over 2 years: Difference = P[(1+R/100)² - 1 - 2R/100] = P(R/100)². Therefore P = Difference × (100/R)². For Q1: P1 = 100 × (100/9)² = 100 × 123.46 = 12346 (approx). For Q2: P2 = 97 × (100/11)² = 97 × 82.64 = 8016 (approx). Since 12346 > 8016, Q1 > Q2.

Multiple choice

Manoj borrowed a certain sum from Sanoj at a certain rate of simple interest for 2 years. He lent this sum to Rakesh at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 4800 as compound interest but paid Rs. 4000 only as simple interest. Find the rate of interest? मनोज ने सनोज से 2 साल के लिए साधारण ब्याज की एक निश्चित दर पर एक निश्चित राशि उधार ली। उसने यह राशि राकेश को समान अवधि के लिए वार्षिक चक्रवृद्धि ब्याज की समान दर पर उधार दी। दो साल के अंत में, उन्हें रु 4800 चक्रवृद्धि ब्याज के रूप में प्राप्त हुआ लेकिन उसने 4000 मात्र साधारण ब्याज के रूप में भुगतान किया ब्याज दर ज्ञात कीजिये?

  1. 40%

  2. 10%

  3. 20%

  4. 15%

  5. 25%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let principal = P, rate = R%. SI for 2 years = 2PR/100 = 4000, so PR = 200000. CI for 2 years = P(1 + R/100)² - P = P[(1 + R/100)² - 1] = 4800. Expanding and using PR = 200000, we find R = 40%. A is correct. Distractors B, C, D, E don't satisfy the interest difference condition.

Multiple choice

Rama borrows two equal sums at the same time at 8% and 7% p.a. respectively. She finds that if she pays the former sum with simple interest on a certain date exactly one year before the latter, she will have to pay in each case the same amount i.e., Rs. 4680. Find the sum? रामा एक ही समय में 8% और 7% प्रति वर्ष की दर से क्रमश दो समान राशि उधार लेता है। उसे पता चलता है कि यदि वह पहली राशि को साधारण ब्याज के साथ एक निश्चित तिथि से ठीक एक वर्ष पहले चुकाती है, तो उसे प्रत्येक मामले में समान राशि रु 4680 का भुगतान करना होगा राशि ज्ञात कीजिए?

  1. Rs 3000 3000 रुपये

  2. Rs 2500 2500 रुपये

  3. Rs 2400 2400 रुपये

  4. Rs 2450 2450 रुपये

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sum be P. At 8% SI for t years: amount = P(1 + 0.08t). At 7% SI for (t+1) years: amount = P(1 + 0.07(t+1)) = P(1 + 0.07t + 0.07) = P(1.07 + 0.07t). Both equal 4680, so P(1 + 0.08t) = P(1.07 + 0.07t). This gives 1 + 0.08t = 1.07 + 0.07t, so 0.01t = 0.07, t = 7 years. Using P(1 + 0.08×7) = 4680: P(1.56) = 4680, P = 4680/1.56 = 3000.

Multiple choice

A, took a certain sum of money from B, as loan at the rate of 7% simple interest per annum. A lends the same amount to C at simple interest of 12% per annum. If at the end of 7 years A makes a profit of Rs 1050, then what amount C had borrowed from A? A, B से ऋण के रूप में प्रति वर्ष 7% साधारण ब्याज की दर पर धन की एक निश्चित राशि लेता है। A, 12% प्रति वर्ष साधारण ब्याज की दर पर C को समान राशि उधार दे देता है। अगर 7 साल के अंत में A को 1050 रुपये का लाभ होता है, तो C ने A से कितनी राशि उधार ली थी?

  1. Rs 3200 3200 रु

  2. Rs 3000 3000 रु

  3. Rs 3500 3500 रु

  4. Rs 3050 3050 रु

  5. None of these. इनमे से कोई नहीं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's profit = (12% - 7%) × P × 7 = 5% × P × 7 = 0.35P = 1050. Principal P = 1050/0.35 = Rs. 3000. C borrowed Rs. 3000 from A.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Find the rate of interest? I - The simple interest of any principal for 3 years is 1200 rupees. II – The compound interest of the same principal for 2 years is 820 rupees. Mark answer-

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For simple interest: SI = P × R × T / 100. From statement I: P × R × 3 / 100 = 1200, so PR = 40000. For compound interest: CI = P(1 + R/100)^2 - P = 820. Combining both gives two equations in P and R which can be solved. Neither statement alone gives both P and R, but together they are sufficient.

Multiple choice

A man invested a sum at the rate of 20% per annum compounded annually and after two years he reinvested the half of the initial amount. The man got Rs. 1080 as interest after three years, find the amount received by him if he invested the same sum at 10% per annum on simple interest for 2 years? एक व्यक्ति ने एक राशि को 20% वार्षिक चक्रवृद्धि की दर से निवेश किया और दो वर्ष बाद उसने प्रारंभिक राशि का आधा पुनर्निवेश किया। आदमी को 1080 रु 3 वर्ष के बाद ब्याज के रूप में, प्राप्त हुआ उसके द्वारा प्राप्त राशि ज्ञात कीजिए यदि वह समान राशि को 10% प्रति वर्ष की दर से साधारण ब्याज पर 2 वर्ष के लिए निवेश करता है?

  1. Rs. 2400 रु. 2400

  2. Rs. 2450 रु. 2450

  3. Rs. 2750 रु. 2750

  4. Rs. 2600 रु. 2600

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial sum = P. After 2 years at 20% compound interest: amount = P(1.2)² = 1.44P. Half of initial amount (P/2) is reinvested for 1 more year at 20%: interest = P/2 × 0.2 × 1 = 0.1P. Total interest after 3 years = (1.44P - P) + 0.1P = 0.44P + 0.1P = 0.54P = 1080. So P = 1080/0.54 = 2000. Simple interest at 10% for 2 years: SI = 2000 × 0.1 × 2 = 400. Total amount = 2000 + 400 = 2400. Options B (2450), C (2750), and D (2600) are incorrect amounts.

Multiple choice

The compound interest on a certain sum at a certain rate of interest per annum for the second year and third year are Rs.3300 and Rs.3630 respectively. What is the amount obtained after 2.5 years when the same sum is lent at the same rate of interest compounded yearly? एक निश्चित राशि पर दूसरे वर्ष और तीसरे वर्ष के लिए एक निश्चित ब्याज दर पर चक्रवृद्धि ब्याज क्रमशः 3300 रुपये और 3630 रुपये है। 2.5 वर्ष के बाद प्राप्त राशि क्या है जब समान राशि को समान वार्षिक चक्रवृद्धि ब्याज दर पर उधार दिया जाता है?

  1. Rs 37215 37215 रुपये

  2. Rs 36300 36300 रुपये

  3. Rs 38115 38115 रुपये

  4. Rs 36000 36000 रुपये

  5. Rs 34728 34728 रुपये
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Compound interest for 3rd year is 3630 and for 2nd year is 3300. The difference is 3630 - 3300 = 330, which is the interest on 3300 at rate r%. So 330 = 3300 × r/100, giving r = 10%. Amount after 2 years at 10% CI = P(1.1)² where 2nd year CI = P × 1.1 × 0.1 = 3300, so P = 33000. Amount after 2.5 years = 33000(1.1)² × 1.05 = 36300 × 1.05 = 38115.

Multiple choice

What is the rate of interest per annum? प्रति वर्ष ब्याज दर क्या है? Statement I An amount double itself at SI in 10 years Statement II The difference between SI and CI on an amount of Rs.20,000 in 2 years is Rs.200. Statement III The CI accured in 9 years is more than the amount. कथन I. एक राशि 10 वर्षों में साधारण ब्याज पर अपने से दुगनी हो जाती है कथन II. 2 वर्षों में 20,000 रुपये की राशि पर SI और CI के बीच अंतर 200 रुपये है। कथन III. 9 वर्षों में अर्जित चक्रवृद्धि ब्याज राशि से अधिक है।

  1. Either I or II is sufficient या तो I या II पर्याप्त है

  2. Both I and II are sufficient I और II दोनों पर्याप्त हैं

  3. Both II and III are sufficient II और III दोनों पर्याप्त हैं

  4. Either I or III is sufficient या तो I या III पर्याप्त है

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: P doubles at SI in 10 years means P + P×r×10/100 = 2P → Pr/10 = P → r = 10%. Statement II: For P = 20000, CI - SI = 200. CI - SI = P[(1 + r/100)² - 1] - Pr×2/100 = P[r²/10000] = 20000 × r²/10000 = 2r²/100. Setting 2r²/100 = 200 → r² = 10000 → r = 10%. Statement III: CI > Principal in 9 years doesn't directly give r. Both Statement I and Statement II individually give r = 10%, so either one is sufficient. Option A is correct.

Multiple choice

A man invests a part of Rs 4000 at 5% p.a. S.I. and the remaining at 6% p.a. Simple Interest. The 5% investment yields interest Rs 145 more than the part invested at 6% after 1 Yr. Find the amount invested at 6% p.a. rate? एक आदमी 4000 रुपये का एक हिस्सा 5% प्रति वर्ष की दर से साधारण ब्याज पर निवेश करता है। और शेष 6% प्रति वर्ष की दर से निवेश करता है 1 वर्ष के बाद 5% के निवेश पर 6% की दर से निवेश किए गए हिस्से से 145 रुपये अधिक ब्याज मिलता है। 6% प्रति वर्ष की दर से निवेश की गई राशि ज्ञात कीजिए।

  1. Rs 120 120 रुपये

  2. Rs 160 160 रुपये

  3. Rs 150 150 रुपये

  4. Rs 400 400 रुपये

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let amount at 6% be x. Then amount at 5% is (4000 - x). Interest at 5% = 0.05(4000 - x) = 200 - 0.05x. Interest at 6% = 0.06x. 'The 5% investment yields interest Rs 145 more than the part invested at 6%' means 200 - 0.05x = 0.06x + 145, so 55 = 0.11x, x = 500. Interest at 5% = 200 - 25 = 175. Interest at 6% = 30. Difference = 145. This matches. But 500 is not in options A-D. Option E 'None of these' is correct.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए। Quantity I : Find the interest earned after 3 years, if a person invests Rs. 12000 at C.I. at the rate of 10% per annum. Quantity II : Find the interest earned after 3 years, if a person invests Rs. 30800 at S.I. at the rate of 20% per annum. मात्रा I : 3 साल बाद अर्जित ब्याज ज्ञात कीजिए, यदि कोई व्यक्ति 12000 रुपये प्रति वर्ष 10% की दर से चक्रवृद्धि ब्याज पर निवेश करता है। मात्रा II: 3 साल बाद अर्जित ब्याज ज्ञात कीजिए, यदि कोई व्यक्ति 30800 रुपये साधारण ब्याज दर पर 20% प्रति वर्ष की दर से निवेश करता है।

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I < Quantity II मात्रा I < मात्रा II

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or relation can't be established. मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: CI for 3 years at 10% on Rs 12000 = 12000[(1.10)³ - 1] = 12000(1.331 - 1) = 12000 × 0.331 = Rs 3972. Quantity II: SI for 3 years at 20% on Rs 30800 = 30800 × 20% × 3 = 30800 × 0.6 = Rs 18480. Since 3972 < 18480, Quantity I < Quantity II. Option C is correct.

Multiple choice

A person borrowed a certain sum at 10% p.a. for three years, interest being compounded annually. At the end of two years, he repaid a sum of Rs. 6634 and at the end of the third year, he cleared off the debt by paying Rs. 13,200. What was the sum borrowed by him? एक व्यक्ति ने एक निश्चित राशि को 10% प्रति वर्ष की चक्रवृद्धि ब्याज पर तीन वर्ष के लिए उधार लिया। दो साल के अंत में, उसने 6634 रुपये की राशि का भुगतान किया और तीसरे वर्ष के अंत में, उसने 13,200 रुपये का भुगतान करके कर्ज खत्म किया तो उसके द्वारा उधार ली गई राशि कितनी थी?

  1. Rs. 16,400 रु. 16,400

  2. Rs. 15,400 रु. 15,400

  3. Rs. 15,600 रु. 15,600

  4. Rs. 16,500 रु. 16,500

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the borrowed sum be P. After 2 years at 10% compound interest: P(1.10)² = 1.21P. After paying Rs. 6634, remaining debt = 1.21P - 6634. In the third year, this grows to: (1.21P - 6634) × 1.10 = 13200. Solving: 1.331P - 7297.4 = 13200, so 1.331P = 20497.4, giving P = Rs. 15400 (approximately). This is the original sum borrowed.

Multiple choice

A sum of money is put at compound interest for 2 years. What is the rate of interest per annum? Statement I: If the same amount of money is put at simple interest for three years then the amount of interest is Rs.600 more than the interest amount calculated on CI at the end of 2 years. Statement II: The simple interest on the same sum at the end of four years is Rs.3200 Statement III: Sum of money becomes 4 times in two years at compound interest

  1. Either statement III alone or statements I and II together are sufficient.

  2. Only statement III is sufficient.

  3. Statement I and Statement III together are sufficient.

  4. Only statement I, II, and III together are sufficient.

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement III: Sum becomes 4 times in 2 years at CI, so (1+r/100)²=4, which gives 1+r/100=2, so r=100%. This alone is sufficient. Alternatively, using Statement I and II together: Let P be principal. From II, SI for 4 years = 3200, so 4PR/100 = 3200, PR=80000. From I, SI(3y) - CI(2y) = 600. 3PR/100 - P[(1+r/100)²-1] = 600. Substituting PR=80000 gives r=100%. Either III alone OR I and II together work.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer- What is the rate of interest? I. The amount doubles itself in 8 years. II. C.I. earned on a certain amount in 2 years is more than the simple interest for the same period by Rs. 345

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I alone is sufficient. If amount doubles in 8 years under simple interest, then interest = principal in 8 years. Rate = (100 * Interest) / (Principal * Time) = (100 * P) / (P * 8) = 100/8 = 12.5% per annum. Statement II is not sufficient because it only tells us the difference between compound and simple interest (Rs. 345) over 2 years, but we need the principal amount to find the rate.

Multiple choice

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer- Find the compound interest on Rs. 12000? I. The rate of interest is 10% per annum. II. The difference between C.I. and S.I. is Rs. 70.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find compound interest, we need: principal (given as Rs. 12000), rate (Statement I gives 10%), and time period. Statement I alone only provides the rate - we still need the time duration. Statement II gives the difference between CI and SI as Rs. 70, but without knowing either the rate or time, this cannot be used to find the CI. Even combining both statements, we're missing the crucial time period variable. The formula for CI-SI difference involves time, and without it, we cannot determine the actual compound interest amount.