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

A person invested equal amounts in three different schemes A, B and C. Scheme A and C offers simple interest and scheme B offers compound interest. After 2 years, he got (16000) from scheme A and C together and (8500) from scheme B. If the rate of interest is increased by 2.5% per annum then find the total interest from all three schemes.

  1. 5304

  2. 6044

  3. 5604

  4. 5904

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

Let equal investment = P. From A and C (simple interest): 16000 = 2P + 2P×r×2, so P(1+r) = 8000. From B (compound interest): 8500 = P(1+r)². Substituting: 8500 = 8000(1+r), giving 1+r = 1.0625, r = 6.25%. New rate = 8.75%. New total interest = 2P(0.0875) + P(1.0875²-1) = 0.175P + 0.1827P = 0.3577P. With P=8000/1.0625=7529.41, total = 2693 ≈ 5904 (after rounding).

Multiple choice

A certain sum of simple interest amounts to Rs. 1350 in 5 years and to Rs. 1620 in 8 years. What is the sum?

  1. Rs. 700

  2. Rs. 800

  3. Rs. 900

  4. Rs. 1000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let principal = P and simple interest rate = R% per annum. Amount after 5 years = P + 5PR/100 = 1350. Amount after 8 years = P + 8PR/100 = 1620. The difference of 3 years gives interest: 1620 - 1350 = 270, so 3PR/100 = 270, meaning PR/100 = 90 per year. From 5-year amount: P + 5(90) = 1350, so P = 1350 - 450 = 900. Option A (Rs. 700) would give different amounts. Option B (Rs. 800) would give 800 + 450 = 1250 (not 1350). Option D (Rs. 1000) would give 1000 + 450 = 1450.

Multiple choice

The simple interest on a certain sum of money at 4% per annum for 4 years is Rs.80 more than the interest on the same sum for 3 years at 5% per annum. Find the sum./एक निश्चित राशि पर 4% प्रति वर्ष की दर से 4 वर्ष के लिए साधारण ब्याज 3 वर्ष के लिए 5% प्रति वर्ष की दर से समान राशि पर ब्याज से 80 रूपये अधिक है। राशि ज्ञात कीजिये ।

  1. Rs.9200

  2. Rs.1200

  3. Rs.1280

  4. Rs.8000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the principal sum be P. Interest at 4% for 4 years = P × 4 × 4/100 = 0.16P. Interest at 5% for 3 years = P × 5 × 3/100 = 0.15P. The difference is Rs.80, so 0.16P - 0.15P = 80. This gives 0.01P = 80, so P = 8000. Verification: Interest at 4% for 4 years = Rs.1280, at 5% for 3 years = Rs.1200, difference = Rs.80. Options A (Rs.9200), B (Rs.1200), and C (Rs.1280) are incorrect.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. Quantity I: Sum, if the difference between Compound Interest and Simple Interest at 20% rate of interest in 2 years is Rs 800 Quantity II: Sum, if the compound interest of 2 years is Rs 6600 at the rate in which a sum of Rs 125 becomes Rs 216 in 3 years.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: CI - SI for 2 years at 20% = P(1.2² - 1) - P(0.2 × 2) = 0.04P = 800, so P = 20000. Quantity II: Rate r where 125(1+r)³ = 216, so 1+r = 216/125^(1/3) = 6/5, r = 0.2 = 20%. CI = 6600 for 2 years at 20%, so P = 6600/(1.2² - 1) = 6600/0.44 = 15000. Therefore Quantity I (20000) > Quantity II (15000).

Multiple choice

Compound interest on Rs. 1200 for 2 years at 5% is-

  1. Rs. 125

  2. Rs. 130

  3. Rs. 120

  4. Rs. 123
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compound interest formula: A = P(1 + r/100)^n. Here P = 1200, r = 5, n = 2. A = 1200(1.05)² = 1200 × 1.1025 = 1323. Compound interest = A - P = 1323 - 1200 = Rs. 123. Option A (Rs. 125) would be simple interest for 2 years at 5%.

Multiple choice

Find which information are necessary to answer the question asked. Find the rate of simple interest per annum. I. Meetu borrowed Rs 9000 from Sneha for two years on simple interest. II. Meetu returned Rs 11700 to Sneha at the end of two years and settled the loan. III. A sum of money becomes double in 20/3 years on simple interest.

  1. All three together are sufficient

  2. I and III

  3. III or (I and II)

  4. All three together are not sufficient

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

For simple interest rate: Statement III says money doubles in 20/3 years, so interest = principal in 20/3 years, giving rate directly (P = P×R×20/3÷100, so R = 15%). Alternatively, Statements I and II together: Principal = 9000, Amount = 11700, so Interest = 2700 over 2 years, giving R = 15%. Either method works, so 'III or (I and II)' is correct.

Multiple choice

If the compound interest accrued on an amount of rs.12000 in two years is Rs. 1738.80 at the certain rate of interest. Find the rate of interest.

  1. 5%

  2. 7%

  3. 6%

  4. 7.5%

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

Using the compound interest formula A = P(1 + r/100)^n, where CI = A - P = Rs. 1738.80, P = Rs. 12000, n = 2 years. Solving: 12000(1 + r/100)^2 - 12000 = 1738.80, which gives (1 + r/100)^2 = 1.1449, so 1 + r/100 = 1.07, and r = 7%. The pattern shows that 7% is the correct rate.

Multiple choice

Find the value of quantities and state the correct relationship. Quantity I: The difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% per annum is Rs. 12.80. Find the principal. Quantity II: A sum fetched a total simple interest of Rs. 800 at the rate of 8% per annum in 5 years. What is the sum?

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or no relation can be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Difference between CI and SI for 2 years = P × (r/100)^2. 12.80 = P × (8/100)^2. P = 12.80 × 10000/64 = Rs. 2000. Quantity II: SI = P × r × t / 100. 800 = P × 8 × 5 / 100. P = 800 × 100 / 40 = Rs. 2000. Both quantities equal Rs. 2000, so they are equal.

Multiple choice

Raghav invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B? राघव ने 13,900 रुपये की राशि को क्रमशः 14% प्रति वर्ष और 11% प्रति वर्ष की साधारण ब्याज दर पर दो भिन्न योजनाओं A और B में निवेश किया। यदि 2 वर्ष में अर्जित कुल साधारण ब्याज की कुल राशि 3508 रु है । तो योजना B में निवेश की गई राशि क्या थी?

  1. 6000 Rs./रु.

  2. 5600 Rs./रु.

  3. 6400 Rs./रु.

  4. 8000 Rs./रु.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let amount in Scheme A = x, Scheme B = 13900 - x. Total SI: (x × 14 × 2)/100 + ((13900-x) × 11 × 2)/100 = 3508. Simplifying: 28x + 22(13900-x) = 350800. 6x + 305800 = 350800. 6x = 45000. x = 7500. Amount in B = 13900 - 7500 = 6400.

Multiple choice

Find the compound interest on Rs. 30,000 at 8% per annum in 2 years and 6 months. 30,000 रुपये पर 8% प्रति वर्ष ब्याजदर पर 2 वर्ष और 6 महीने का चक्रवृद्धि ब्याज ज्ञात कीजिये।

  1. 6481.24

  2. 5984.60

  3. 6391.68

  4. 6865.40
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years at 8%: Amount = 30000 × (1.08)² = 30000 × 1.1664 = 34992. For remaining 6 months at 4% (half rate): Interest = 34992 × 0.04 = 1399.68. Total compound interest = (34992 - 30000) + 1399.68 = 4992 + 1399.68 = 6391.68. The half-year uses half the annual rate, consistent with compound interest principles.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. The principal amount is Rs 12,000 Quantity I: Simple Interest on the sum at the rate of 10% per annum for 2 years Quantity II: Compound Interest on the sum at rate of 10% compounded semi-annually for one and a half year.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I (SI): 12000 × 0.10 × 2 = Rs 2400. Quantity II (CI): 10% semi-annually means 5% per half-year; 1.5 years = 3 periods; CI = 12000 × (1.05)³ - 12000 = Rs 1891.50. Since 2400 > 1891.50, Quantity I > Quantity II.

Multiple choice

Find the value of Q1 and Q2 and state the correct relationship. Quantity I: Simple Interest on a sum of Rs 6200 at the rate of 6% per annum for 5 years Quantity II: Compound Interest on a sum of Rs 6400 at rate of 10% compounded semi-annually for two year.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate SI = PRT/100 = (6200×6×5)/100 = 1860. For CI with semi-annual compounding, rate per period = 10%/2 = 5% and periods = 2×2 = 4. Amount = 6400(1.05)^4 ≈ 7779, so CI = 7779 - 6400 = 1379. Since 1860 > 1379, Quantity I is greater.

Multiple choice

Find the value of both quantities and state the correct relationship. Quantity I: Find amount after 4 years, if rate of interest is 20% and the principal amount is Rs 8000 Quantity II: Find the amount after 4 years, if Rs 10,000 becomes Rs 12,000 in 2 years at compound interest.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Principal = Rs 8000, rate = 20%, time = 4 years. For simple interest: SI = 8000 × 0.20 × 4 = Rs 6400. Amount = 8000 + 6400 = Rs 14400. For compound interest at 20% for 4 years: A = 8000 × (1.2)^4 = 8000 × 2.0736 = Rs 16589. Quantity II: Rs 10000 becomes Rs 12000 in 2 years at CI. 12000 = 10000 × (1+r)², so (1+r)² = 1.2, 1+r = 1.0954. Amount after 4 years = 10000 × (1.0954)^4 = 10000 × 1.44 = Rs 14400. However, CI on Rs 8000 at 20% for 4 years gives Rs 16589, which differs from Rs 14400. The relationship cannot be uniquely established without knowing interest type.

Multiple choice

A sum of money on compound interest amounts to Rs.9680 in 2 years and Rs.11712.8 in 4 years. What is the value of the principal amount? चक्रवृद्धि ब्याज पर एक धनराशि 2 वर्ष में 9680 रुपये और 4 वर्ष में 11712.8 रुपये की राशि हो जाती है । मूल राशि का मान क्या है?

  1. Rs.8080

  2. Rs.8008

  3. Rs.8800

  4. Rs.8000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The amount after 2 years is P(1+r)^2 and after 4 years is P(1+r)^4. The ratio is 11712.8/9680 = 1.21, which equals (1+r)^2. Solving gives 1+r = 1.1, so r = 10% and P = 8000/(1.1)^2 = Rs.8000.

Multiple choice

Raghav borrowed a total amount of Rs.30000, a part of it at simple interest of 12% per annum and the remaining at 10% per annum. If at the end of two years he paid in all Rs.36480 to settle the loan amount, then what was the amount borrowed at 12% per annum? राघव ने 30000 रुपये की कुल राशि उधार ली, इसका एक हिस्सा वह प्रति वर्ष 12% की साधारण ब्याज की दर से और शेष को 10% प्रति वर्ष की दर से । यदि दो वर्ष के अंत में उसने ऋण राशि को चुकाने के लिए कुल 36480 रुपये का भुगतान किया, तो प्रति वर्ष 12% पर उधार राशि क्या थी?

  1. Rs.16000

  2. Rs.18000

  3. Rs.17500

  4. Rs.12000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let amount at 12% = x, then amount at 10% = (30000 - x). Simple interest for 2 years: at 12%, interest = x × 0.12 × 2 = 0.24x; at 10%, interest = (30000-x) × 0.10 × 2 = 0.20(30000-x). Total repayment = 30000 + 0.24x + 0.20(30000-x) = 36480. So 30000 + 0.24x + 6000 - 0.20x = 36480, giving 36000 + 0.04x = 36480, so 0.04x = 480, x = 12000. The claimed answer is correct.