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 sum of Rs 3500 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. Find the interest on each part? 3500 रुपये की राशि को दो भागों में इस प्रकार विभाजित किया जाता है,जिससे पहले भाग में 8% प्रति वर्ष साधारण ब्याज पर और दूसरे भाग पर 6% प्रति वर्ष साधारण ब्याज के बराबर होता है। प्रत्येक भाग पर ब्याज ज्ञात कीजिये?

  1. Rs. 600

  2. Rs. 100

  3. Rs. 80

  4. Rs. 120

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

Let the two parts be Rs. x at 8% and Rs. (3500-x) at 6%. Equal interest means: x × 8% = (3500-x) × 6%. Solving: 0.08x = 210 - 0.06x, so 0.14x = 210, giving x = 1500. First part: Rs. 1500 at 8% gives interest of Rs. 120. Second part: Rs. 2000 at 6% also gives interest of Rs. 120. The interest on each part is Rs. 120.

Multiple choice

If the amount received at the end of 2nd and 3rd year at Compound Interest on a certain Principal is Rs 33708, and Rs 35730.48 respectively, what is the rate of interest? यदि दूसरे और तीसरे वर्ष के अंत में एक निश्चित मूलधन पर चक्रवृद्धि ब्याज पर प्राप्त राशि क्रमशः 33708 रुपये और 35730.48 रुपये है, तो ब्याज की दर क्या है?

  1. 6%

  2. 18%

  3. 12%

  4. 10%

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

Let amount after 2 years = A₂ = Rs. 33708 and after 3 years = A₃ = Rs. 35730.48. The interest earned in the 3rd year = 35730.48 - 33708 = Rs. 2022.48. Rate r = (2022.48 / 33708) × 100 = 6%. This is verified by checking 33708 × 1.06 = 35730.48.

Multiple choice

In how many years will the sum becomes 5 times of itself at the rate of 5% per annum simple interest? 5% वार्षिक साधारण ब्याज की दर से कितने वर्षों में राशि स्वयं का 5 गुना हो जाएगी?

  1. 80 years 80 वर्ष

  2. 50 years 50 वर्ष

  3. 25 years 25 वर्ष

  4. 12.5 years 12.5 वर्ष

  5. Cannot be determined निर्धारित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For sum to become 5 times itself at simple interest, interest = 4P. Using SI = P×R×T/100: 4P = P×5×T/100. Solving: 4 = 5T/100, so T = 400/5 = 80 years. Option A is correct.

Multiple choice

If the difference between the compound and simple interest on a sum for 3 years at the rate of 10% per annum is Rs. 77.5 then find the sum invested? यदि किसी राशि पर 10% प्रति वर्ष की दर से चक्रवृद्धि और साधारण ब्याज के बीच का अंतर 3 वर्ष के लिए रु. 77.5 तो निवेश की गई राशि ज्ञात कीजिए?

  1. Rs. 3500 3500 रु .

  2. Rs. 2500 2500 रु .

  3. Rs. 4000 4000 रु .

  4. Rs. 1500 1500 रु .

  5. Rs 4200 4200 रु .
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Difference between CI and SI for 3 years = P×(R/100)²×(3 + R/100). Substituting: 77.5 = P×(10/100)²×(3 + 10/100) = P×0.01×3.1 = 0.031P. Solving: P = 77.5/0.031 = 2500. Option B is correct.

Multiple choice

A sum fetched a total simple interest of Rs 1200 at the rate of 7.5% in 4 years. What is the sum (in Rs)? एक राशि द्वारा 4 साल में 7.5% वर्ष की दर से 1200 रु साधारण ब्याज प्राप्त हुआ । वह राशि (रु में) क्या है?

  1. 4000

  2. 6000

  3. 8000

  4. 7500

  5. 5600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the simple interest formula P = (SI × 100)/(R × T). Substituting SI = 1200, R = 7.5%, T = 4 years gives P = 120000/30 = 4000. Option A is correct.

Multiple choice

The simple and compound interest that can be earned in two years at the same rate is Rs 1500 and Rs 1575 respectively. What is the rate (% per annum) of interest? दो वर्षों में समान दर से अर्जित किया गया साधारण और चक्रवृद्धि ब्याज क्रमशः 1500 रुपये और 1575 रुपये है। ब्याज की दर (% प्रति वर्ष) क्या है?

  1. 8

  2. 10

  3. 12

  4. 5

  5. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2 years, the extra interest in CI over SI equals interest on first year's interest. Yearly SI = 1500/2 = 750. Difference = 1575 - 1500 = 75. Rate = (75/750) × 100 = 10%. Option B is correct.

Multiple choice

A sum of money at simple interest amounts to Rs.6,000 in 4 years and to Rs.6,750 in 7 years at the same rate per cent p.a. of interest. The sum (in Rs.) is: साधारण ब्याज पर एक राशि 4 वर्षों में 6,000 रुपये और 7 वर्षों में समान दर पर 6,750 रुपये हो जाती है। ब्याज की राशि (रुपये में) है:

  1. 5,100

  2. 4,800

  3. 4,000

  4. 5,000

  5. 3,200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interest for 3 years (7-4) = Rs 6,750 - Rs 6,000 = Rs 750. Annual interest = Rs 750/3 = Rs 250. Principal = Amount after 4 years - Interest for 4 years = Rs 6,000 - Rs 1,000 = Rs 5,000. Verification: Rs 5,000 + 4 × 250 = Rs 6,000 ✓

Multiple choice

A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a. compounded annually and each instalment is Rs. 5,808, then 60% of the total interest (nearest to a Rs.) charged in this scheme is: एक ऋण दो समान वार्षिक किश्तों में वापस किया जाना है। यदि ब्याज दर 10% प्रति वर्ष है और प्रत्येक किस्त रु 5,808 है, तो इस योजना में लिए जाने वाले कुल ब्याज का 60% (लगभग रु.) है:

  1. 911

  2. 913

  3. 917

  4. 922

  5. 925
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For loan repaid in 2 equal installments of Rs 5,808 at 10% p.a.: Loan amount = 5808/(1.1) + 5808/(1.1²) = 5,280 + 4,800 = Rs 10,080. Total repaid = 2 × 5,808 = Rs 11,616. Interest = 11,616 - 10,080 = Rs 1,536. 60% of interest = 0.6 × 1,536 = Rs 921.6 ≈ Rs 922.

Multiple choice

What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly? 50000 की धनराशि के लिए 8% वार्षिक व्याज की दर पर अर्धवार्षिक रूप से चक्र्वृधि होने वाले और वार्षिक रूप से चक्रवृधि होने वाले एक वर्ष के व्याज के बीच अंतर (रूपये में) है?

  1. 80

  2. 50

  3. 70

  4. 100

  5. 85
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For Rs 50,000 at 8% p.a. for 1 year: Yearly compounding gives interest = 50,000 × 0.08 = Rs 4,000. Half-yearly compounding: rate = 4%, 2 periods, amount = 50,000 × 1.04² = 54,080, interest = Rs 4,080. Difference = 4,080 - 4,000 = Rs 80.

Multiple choice

A sum of money is invested at a certain rate of compound interest payable annually. The interests in two successive years are Rs 225 and Rs 240 . Find the interest in third year ? एक राशि को चक्रवृद्धि ब्याज की एक निश्चित दर पर वार्षिक रूप से देय होने पर निवेश किया जाता है। लगातार दो वर्षों में ब्याज 225 रुपये और 240 रुपये है। तीसरे वर्ष में ब्याज ज्ञात कीजिये?

  1. 256

  2. 290

  3. 260

  4. 265

  5. 280
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In compound interest, interest increases by the rate each year. Interest year 1 = 225, interest year 2 = 240. Increase = 240 - 225 = 15. Rate = 15/225 = 1/15 = 6.67%. Interest year 3 = 240 + (240 × 1/15) = 240 + 16 = 256.

Multiple choice

At what rate percent per annum will a sum of Rs. 1,000 amount to Rs. 1,102.50 in 2 years at compound interest? किस दर पर प्रतिशत प्रतिवर्ष की राशि रु. 1,000 राशि से रु. चक्रवृद्धि ब्याज पर 2 वर्षों में 1,102.50?

  1. 5

  2. 5.5

  3. 6

  4. 6.5

  5. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using CI formula: A = P(1 + r/100)^t. 1102.50 = 1000(1 + r/100)². Dividing: 1.1025 = (1 + r/100)². Taking square root: 1.05 = 1 + r/100. Therefore r/100 = 0.05, so r = 5%.

Multiple choice

Ram borrowed Rs. 10000 from Sachin at simple interest. After 4 years, Sachin received Rs. 5000 more than the amount given to Ram on loan. Find the rate of interest. राम ने सचिन से साधारण ब्याज पर 10000 रुपये उधार लिए। 4 वर्ष बाद सचिन को राशि से 5000 अधिक प्राप्त हुए । ब्याज दर ज्ञात कीजिए।

  1. 12.5%

  2. 25%

  3. 20%

  4. 4%

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

Principal = Rs. 10000, Time = 4 years, Simple Interest = Rs. 5000. SI = P × R × T / 100, so 5000 = 10000 × R × 4 / 100. This gives 5000 = 400R, therefore R = 5000/400 = 12.5%.

Multiple choice

On simple interest, a certain sum becomes ₹59,200 in 6 years and ₹72,000 in 10 years. If the rate of interest had been 2% more, then in how many years would the sum have become ₹76,000 ?

  1. 10

  2. 9

  3. 8

  4. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference in amount over 4 years (from year 6 to year 10) is ₹12,800, which equals P×R×4/100. This gives P×R/100 = ₹3,200. Using the 6-year value: 59,200 = P + 6×3,200, so P = ₹40,000 and R = 8%. At 2% more (10% rate), the time t for ₹76,000 is: 76,000 = 40,000 + 40,000×10×t/100, giving t = 9 years.