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

Alok invested a sum of money for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120. For how many years was the sum invested? आलोक एक धनराशि को निश्चित वर्षों की संख्या के लिए 8% वार्षिक साधारण ब्याज की दर से निवेशित करता है जोकि 180 रु. प्रदान करता है | समान धनराशि को समान वर्षों की संख्या के लिए 4% वार्षिक साधारण ब्याज की दर से 120 रु. प्राप्त करता है | कितने वर्षों के लिए राशि निवेशित रही ?

  1. 25 years/वर्ष 4 months/माह

  2. 40 years/वर्ष 4 months/माह

  3. 33 years/वर्ष

  4. 25 years/वर्ष
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the principal be P and time be t years. At 8% simple interest, amount is P(1 + 8t/100) = 180. At 4%, P(1 + 4t/100) = 120. Dividing the equations: (1 + 8t/100) / (1 + 4t/100) = 180/120 = 3/2. This gives 2 + 16t/100 = 3 + 12t/100, so 4t/100 = 1, therefore t = 25 years.

Multiple choice

A sum of Rs. 50440 is divided into three parts and lent out for 2 years, 3 years and 4 years respectively. If the rate of compounded interest be 5% and the amount of each part become same after the completion of time in each case, find the difference between the second and first part. 50440 रू. की एक धनराशि तीन भागों में बांटी जाती है और क्रमशः 2 वर्ष, 3 वर्ष और 4 वर्ष के लिए उधार दी जाती है। यदि चक्रवृद्धि ब्याज की दर 5ः है और प्रत्येक स्थिति में समयावधि पूर्ण होने के पश्चात प्रत्येक भाग से प्राप्त धनराशि समान है। दूसरे और पहले भाग में अन्तर ज्ञात कीजिए।

  1. Rs. 800

  2. Rs. 820

  3. Rs. 840

  4. Rs. 880
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let final amount = A. First part (2 years): A = P₁(1.05)², so P₁ = A/(1.05)². Second part (3 years): P₂ = A/(1.05)³. Third part (4 years): P₃ = A/(1.05)⁴. Setting P₁ + P₂ + P₃ = 50440 and solving gives the values. Difference between second and first parts is Rs. 840.

Multiple choice

A sum of Rs. 11850 was divided in Rajesh, Ranjeet and Ramesh. Rajesh invests his money in a bank for 3 years which gives 12% rate of interest, Ranjeet invests his money in a bank for 2.5 years which gives 15% rate of interest and Ramesh invests his money in a bank for 1.5 years which gives 20% rate of interest. If they get equal interest, find the amount given to Ramesh. 11850 रूपये का एक धन राजेश, रंजीत तथा रमेश में बांटा गया। राजेश ने अपना धन एक बैंक में 3 वर्षों के लिए निवेश किया जो 12% की ब्याज दर देता है, रंजीत ने अपना धन एक बैंक में 2.5 वर्षों के लिए निवेश किया जो 15% की ब्याज दर देता है तथा रमेश ने अपना धन एक बैंक में 1.5 वर्षों के लिए निवेश किया जो 20% की ब्याज दर देता है। यदि उन्हें समान ब्याज प्राप्त हुआ, तो रमेश को मिलने वाला धन ज्ञात कीजिये ।

  1. Rs. 3000

  2. Rs. 4000

  3. Rs. 4200

  4. Rs. 4500
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For equal simple interest, Principal × Time × Rate must be equal. Rajesh: P₁×3×12 = 36P₁. Ranjeet: P₂×2.5×15 = 37.5P₂. Ramesh: P₃×1.5×20 = 30P₃. Let equal interest = 1110k. Then P₁=30.83k, P₂=29.6k, P₃=37k. Sum = 97.43k = 11850, so k≈121.6. Thus P₃≈37×121.6 ≈ 4500.

Multiple choice

Each of these questions consists of a question followed by information in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question. Find the compound interest of 2 years and 3 months compounded annually- Statement I:-If the principal is invested for 3 years at SI it generates a interest equal to 1200 rs. Statement II- CI of second years is 480 Rs. Statement III- CI of third year is 96 Rs more than CI of second year.

  1. Any two

  2. I and (II or III)

  3. II and III

  4. I and III

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

Statement I gives principal and simple interest rate (SI = PRT, so rate = 1200/(3P)). Statement II gives CI for year 2, or Statement III gives CI difference between years 2 and 3. Either II or III with I allows finding rate and calculating CI for 2 years 3 months.

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. $Quantity I: Suresh took a loan from the bank at 12% p.a simple interest. After 3 years he had to pay back Rs. 16,200 as interest. Find the loan taken by Suresh from the bank. Quantity II: Amount after 2 years for a principal of Rs 35,000 at an interest rate of 10% compounded annually.$

  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: Simple Interest = P × R × T / 100. 16200 = P × 12 × 3 / 100, so P = 16200 × 100 / 36 = Rs 45000. Quantity II: Compound Interest Amount = 35000 × (1 + 10/100)² = 35000 × 1.21 = Rs 42350. Since 45000 > 42350, Quantity I > Quantity II, so Option A is correct.

Multiple choice

Each of the questions below consists of a question and some statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A person borrowed some money at compound interest for 2 years. What will be the amount required to return after 2 years? Statement I: If the amount was borrowed at simple interest, then after 5 years Rs 600 was required to pay as simple interest. Statement II: The rate of interest is 6% per annum Statement III: The sum of money borrowed is 10 times the amount required to be paid as simple interest after 2 years.

  1. II and I or III

  2. All three together are sufficient

  3. II and III together

  4. I and II together

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

Statement II gives rate = 6%. Statement I: If borrowed at simple interest, SI after 5 years = Rs 600. Using SI = P×R×T/100, we get 600 = P×6×5/100, so P = Rs 2000. For compound interest at 6% for 2 years: A = P(1 + R/100)² = 2000(1.06)² = Rs 2247.20. Statements I and II together are sufficient. Statement III relates P to SI after 2 years but without the rate, is insufficient alone. Option D (I and II together) is correct.

Multiple choice

Which information is/are sufficient to answer the questions asked? A sum of money is put at CI. Find the rate percent when the interest is reckoned yearly. I. The ratio of SI to CI at the end of 3 years on the same sum and same rate of interest is 300: 331. II. If the same sum is put at SI for 5 years on the same rate of interest then the SI will be 50% less than the principal amount. III. The difference between CI and SI at the end of 2 years on the same sum and same rate of interest is Rs 200.

  1. Any two of them

  2. III and (I or II)

  3. I or II alone is sufficient

  4. II or (I and III)

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

Statement II directly gives the rate: SI for 5 years is 50% of principal, so 5r/100 = 50/100, giving r = 10%. Statement I gives the ratio SI/CI = 300/331 after 3 years. For principal P and rate r, SI = 3Pr/100, CI = P(1 + r/100)^3 - P. Setting their ratio equal to 300/331 gives an equation solvable for r. Statement III alone gives CI - SI = Pr^2/10000 for 2 years, but requires P, so not sufficient alone. Therefore, I or II alone is sufficient.

Multiple choice

In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and find which information is/are necessary to answer. The compound interest on a sum of Rs. 8000 is Rs. 2648. Find the rate of interest. Statement I: The simple interest on the same sum at the same rate is Rs. 2400. Statement II: Compound interest is compounded every four months. Statement III: The sum doubles itself in 25 years at the rate of 4% per annum.

  1. Only I and III

  2. All statements together are sufficient

  3. Only I and II

  4. (I and II) or III

  5. All statements together are not sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For CI of Rs. 2648 on Rs. 8000, total = 10648. Statement I (SI = 2400) with Statement II (quarterly compounding) are internally consistent: quarterly rate 5% gives CI ~2648 in 2 years and SI 2400. Statement III (4% rate, doubles in 25 years) is about simple doubling but doesn't help find the rate in our problem. Even I+II don't uniquely determine time. All statements together are insufficient.

Multiple choice

In each of the following questions, a question is followed by two or three statement. Read all the statements and find that which statements are required to answer the question and answer accordingly. What is the rate of interest p.c.p.a? Statement I: Simple Interest accrued in two years on the same amount at the same rate of interest is Rs. 44,000. Statement II: The amount becomes Rs. 15,400 in two years on simple interest. Statement III: Difference between the compound interest and simple interest earned in two years on the amount invested is Rs. 120.

  1. Only I and II

  2. Only II and III

  3. Only II

  4. Only I and III

  5. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P = principal, R = rate. From I: SI for 2 years = 44,000, so P×R×2/100 = 44,000, hence PR = 2,200,000. From III: CI - SI for 2 years = 120. For 2 years, CI-SI = P(R/100)². So P(R/100)² = 120, giving PR²/10,000 = 120, hence PR² = 1,200,000. Dividing PR² by PR gives R = 1,200,000/2,200,000 = 6/11 ≈ 5.45%. Thus I and III are sufficient.

Multiple choice

What was the total compound interest on a sum after three years? Statement I: The interest after one year was Rs.100 and the sum was Rs.1000. Statement II: The difference between simple and compound interest on a sum of Rs.1000 at the end of two years was Rs.10.

  1. If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question

  2. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

  3. If the data either in statement I alone or in statement II alone are sufficient to answer the question.

  4. If the data even in both the statements I and II together are not sufficient to answer the question.

  5. If the data in both the statements I and II together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: Principal = 1000, CI after 1 year = 100 at rate r. So 1000(1 + r) - 1000 = 100, giving 1000r = 100, so r = 10%. CI for 3 years at 10%: 1000[(1.1)^3 - 1] = 1000(1.331 - 1) = 331. Sufficient alone. Statement II: For principal 1000, SI - CI after 2 years = 10. SI = 1000 * 2r = 2000r, CI = 1000[(1+r)^2 - 1] = 1000(2r + r^2) = 2000r + 1000r^2. Difference = 1000r^2 = 10, so r^2 = 0.01, r = 10%. CI for 3 years: 1000[(1.1)^3 - 1] = 331. Also sufficient alone. Either statement gives the answer. Option C is correct.

Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer Quantity I- what sum will fetch a simple interest of Rs 25410 in five and a half years at 6% pa rate of interest. Quantity II- A sum amounts to 90000 after 3 years at compound interest being compounded annually. The amount becomes 112500 the subsequent year. At the same rate of interest Rs 60000 after a year will be

  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 relation can not be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Simple interest formula gives principal P = (25410 × 100) / (6 × 5.5) = 77000. Quantity II: From compound interest data, rate = 25% (112500/90000 - 1). Rs 60000 at 25% for 1 year becomes 60000 × 1.25 = 75000. Since 77000 > 75000, Quantity I > Quantity II.

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. Quantity I: If the S.I. on a sum of money for 2 years at 10% per annum is Rs.100, what is the C.I. on the same sum of money at the same rate and for the same time period? Quantity II: What principal will be amount to Rs.48250 at compound interest in 2 years, the rate of interest for 1st & 2nd year being 6% and 8% respectively?

  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 the relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: SI = P × R × T / 100. 100 = P × 10 × 2 / 100. P = 500. CI = P(1 + R/100)^T - P = 500(1.1)^2 - 500 = 500(1.21) - 500 = 605 - 500 = 105. Quantity II: Principal P. After year 1 at 6%: P × 1.06. After year 2 at 8%: P × 1.06 × 1.08 = P × 1.1448 = 48250. P = 48250 / 1.1448 = 42147. Since 105 < 42147, Quantity I < Quantity II.

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- If the difference between Ci and Si for three years be Rs.1500 on the principal of Rs.30720 then find the rate of interest per annum? Quantity II- If the difference between Ci and Si for three years be Rs.228 on the principal of Rs.46875 then find the rate of interest per annum?

  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

For Quantity I: Using CI-SI difference formula for 3 years, D = P*(r/100)^2*((300+r)/100). Given D=1500, P=30720. Solving: 1500 = 30720*(r/100)^2*((300+r)/100). For Quantity II: D=228, P=46875. 228 = 46875*(r/100)^2*((300+r)/100). Calculating both rates shows Quantity I's rate is greater than Quantity II's rate. Thus, Quantity I > Quantity II is correct.

Multiple choice

A person lent some amount of money at compound interest. Find the rate of interest of the sum of money. A- The value of the amount after 4 years is 24883.2 rupees. B- The money lender would get the sum of 17280 rupees after two years.

  1. if the Statement ‘A’ alone is sufficient to answer the question but the Statement ‘B’ alone is not sufficient

  2. if the Statement ‘B’ alone is sufficient to answer the question but the Statement ‘A’ alone is not sufficient

  3. if both Statement ‘A’ and ‘B’ together are needed to answer the question

  4. if either the Statement ‘A’ alone or Statement ‘B’ alone is sufficient to answer the question

  5. If you cannot get the answer from both the Statements together
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be principal and r be rate. From A: P(1+r)^4 = 24883.2. From B: P(1+r)^2 = 17280. Dividing gives (1+r)^2 = 24883.2/17280 = 1.44, so 1+r = 1.2 and r = 0.2 = 20%. Neither statement alone gives both unknowns, but together they do.

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. \ Quantity I: If the compound interest on a sum of money for 2 years at 10% per annum is Rs.4200, what is the simple interest on the same sum of money at the same rate and for the same time period? \ Quantity II: A certain sum of money will be amount to Rs.48250 at compound interest in 2 years, the rate of interest for 1st & 2nd year being 6% and 8% respectively, how much compound interest earn if rate of compound interest is 6% only?

  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 the relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: CI = P[(1 + 0.10)² - 1] = 4200, solving gives P = 20000. SI = 20000 × 0.10 × 2 = 4000. Quantity II: Amount = P(1.06)(1.08) = 48250, solving gives P ≈ 42536. At 6% only, CI = 42536[(1.06)² - 1] = 42536 × 0.1236 ≈ 5257. Comparing: Quantity I (4000) < Quantity II (5257).