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

Ravi invested Rs. P in a scheme A offering simple interest at 10% p.a. for two years. He invested the whole amount he received from scheme A, in another scheme (B) offering simple interest at 12% p.a. for five years. If the difference between the interests earned from schemes A and B was Rs. 13,00, what is the value of P?

  1. 3000

  2. 3200

  3. 2500

  4. 2200

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

Scheme A: Interest = P × 10% × 2 = 0.2P. Amount received = 1.2P. Scheme B: Interest = 1.2P × 12% × 5 = 0.72P. Difference = 0.72P - 0.2P = 0.52P = 13000. Therefore P = 13000/0.52 = 25000. Wait, this gives P = 25000, not 2500. Checking: 0.52 × 2500 = 1300, not 13000. The question says Rs. 13,00 which is ambiguous - could be 1300 (with comma typo) or 13000. If 1300, then P = 2500.

Multiple choice

Ranjeet borrowed some money at the rate of 4% per annum for the first 3 years, at the rate of 8% per annum for the next 2 years and at the rate of 9% per annum for the period beyond 5 years. If he pays a total simple interest of Rs. 19,550 at the end of 7 years, how much money did he borrow?

  1. 35000

  2. 42500

  3. 38000

  4. 45200

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

Let P be the principal. Total SI = P × 4% × 3 + P × 8% × 2 + P × 9% × 2 = P(0.12 + 0.16 + 0.18) = 0.46P = 19550. So P = 19550/0.46 = 42500. The interest varies over 3 different time periods totaling 7 years.

Multiple choice

On a certain sum, the simple interest in 5 years at the rate of 10 p.c.p.a is Rs. 1200. What will be compound interest on the same sum at eh rate of 10 p.c.p.a after 2 years? मूलधन की एक राशि पर 5 वर्ष में 10 प्र.श.प्र.व. की दर से उपचित साधारण ब्याज 1200 रू. है। समान राशि पर 10 प्र.श.प्र. व. की दर से 2 वर्ष बाद चक्रवृद्धि ब्याज क्या होगा?

  1. Rs. 520

  2. Rs. 535

  3. Rs. 550

  4. Rs. 525

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

SI = P × R × T/100. Given: 1200 = P × 10 × 5/100 → P = 1200 × 100/50 = Rs. 2400. CI for 2 years at 10%: Amount = 2400(1 + 10/100)² = 2400(1.1)² = 2400 × 1.21 = Rs. 2904. CI = 2904 - 2400 = Rs. 504. Since Rs. 504 is not among options A-D, Option E (None of these) is correct.

Multiple choice

The simple interest accrued on a certain principal is Rs 6400 in four years at 8 p.c.p.a.What would be the C.I accured on that principal at 2 p.c.p.a in 2 years? एक मूलधन पर 4 वर्षो में 8% वार्षिक साधारण ब्याज की दर से ब्याज 6400 रू. प्राप्त होता है तो इसी धनराशि पर 2 प्र.श.प्र.व. की दर से चक्रवृद्धि ब्याज 2 वर्षो में क्या होगा ?

  1. 808

  2. 750

  3. 724

  4. 797

  5. 824
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

SI = 6400, t = 4, r = 8%. P = SI / (r × t) = 6400 / (0.08 × 4) = 6400 / 0.32 = 20000. CI for 2 years at 2%: A = 20000(1.02)² = 20000 × 1.0404 = 20808. CI = 20808 - 20000 = 808. Option A is correct.

Multiple choice

If the amount on a certain principal in 3 years at 12% rate of interest compounded annually is rupees 12000, what will be the amount in rupees after the fourth year?

  1. 14330

  2. 15440

  3. 13440

  4. 14550
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The amount after 3 years is Rs. 12000 at 12% compounded annually. For the 4th year, only one more year of interest applies at the same rate. Amount after 4th year = 12000 × 1.12 = Rs. 13440. Simply multiply by 1.12 to add one more year of compound interest.

Multiple choice

If a certain sum of money becomes Rs. 7500 in 3.5 years and Rs. 11250 in 7 years at certain rate of interest at C.I. compounded annually. Then find the principal?

  1. 5500

  2. 4500

  3. 5000

  4. 4000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In compound interest, amounts after successive years form a geometric progression. If the amount after 3.5 years is Rs. 7500 and after 7 years is Rs. 11250, then the ratio A₇/A₃.₅ = 11250/7500 = 1.5. For a geometric progression with 3.5 year gap, this represents (1 + r/100)³·⁵ = 1.5. After 3.5 more years (7 years total), the factor would be 1.5² = 2.25. Working backwards: Principal = 7500/1.5 = 5000, which matches option C.

Multiple choice

Rs.2700 becomes Rs.3600 at a certain rate of interest compounded annually in 5 years. Then find the amount at the end of 15th year.

  1. 6400

  2. 6500

  3. 4500

  4. 6000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The amount formula for compound interest is A = P(1 + r/100)ⁿ. Given that Rs. 2700 becomes Rs. 3600 in 5 years: 3600/2700 = 4/3 = (1 + r/100)⁵. After 15 years (three 5-year periods), the amount will be 2700 × (4/3)³ = 2700 × 64/27 = 6400. This matches option A. The key insight is that 15 years = 3 × 5 years, so we cube the 5-year growth factor.

Multiple choice

If a person invested 6000 at R% S.I for 3 year and same amount at (R + 5)% CI for 2 year and difference between both interest is 60 Rs. then find R ?(in %) यदि किसी व्यक्ति ने 3 वर्ष के लिए R% S.I पर 6000 और उसी वर्ष (R +5)% CI पर 2 वर्ष के लिए निवेश किया है और दोनों के बीच का अंतर 60 रु है तो R खोजें? (% में)

  1. 15

  2. 18

  3. 20

  4. 24

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

SI on ₹6000 for 3 years at R% = (6000 × R × 3)/100 = 180R. CI on ₹6000 for 2 years at (R+5)% = 6000[(1 + (R+5)/100)² - 1] = 6000[(R+5)²/10000 + 2(R+5)/100] = 0.6(R² + 10R + 25) + 120(R+5). This simplifies, and the difference CI - SI = 60 gives R = 15%.

Multiple choice

A sum of Rs.150000 is deposited in a bank at an interest rate of 14% per annum. If the interest is compounded half yearly, find the amount received at the end of 1 year (approximately) बैंक में प्रति वर्ष 14% की ब्याज दर पर 150000 रुपये की राशि जमा की जाती है। यदि ब्याज छमाही रूप से संयोजित है, तो 1 वर्ष (लगभग) के अंत में प्राप्त राशि ज्ञात कीजिए?

  1. Rs.178270

  2. Rs.172200

  3. Rs.171735

  4. Rs.176260

  5. Rs.177300
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

With half-yearly compounding, the annual rate of 14% is split into two periods of 7% each. The formula becomes A = P(1 + r/2)^(2t), which gives 150000 × 1.07^2 = 150000 × 1.1449 ≈ 171735. Options A, B, D, and E are incorrect as they don't account for the proper compound interest calculation.

Multiple choice

Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years, respectively. The difference in the interests was Rs.3080. The sum borrowed were - दो बराबर धनराशि क्रमशः 2 वर्ष और 3 वर्ष के लिए प्रति वर्ष 8% साधारण ब्याज की दर पर उधार ली गई थी। ब्याजों में अंतर 3080 रुपये था। उधार ली गई राशियां थीं

  1. Rs.37950 37950 रु.

  2. Rs.38500 38500 रु.

  3. Rs.40700

  4. 42900 रु.

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

Let the sum borrowed be P. Simple interest for 2 years = P × 8% × 2 = 0.16P. Simple interest for 3 years = P × 8% × 3 = 0.24P. The difference is 0.08P = 3080, so P = 3080 / 0.08 = 38500. The sum borrowed was Rs 38500.

Multiple choice

What is the rate of interest? I. Simple interest accrued in two years on an amount at the same rate of interest is Rs 88000. II. The amount after some years on simple interest is Rs 308000. III. Difference between the compound interest and simple interest earned in two years on the same amount and at the same rate of interest is Rs 240.

  1. Only I and III

  2. Only III

  3. Only II and III

  4. Cannot be answered even including all statement

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

Statement III gives the CI-SI difference for 2 years as Rs.240. The formula for this difference is P×R²/100². Statement I gives 2-year SI as Rs.88000, meaning P×R×2/100 = 88000, so P×R = 44,00,000. From these two equations, we can solve for R (rate comes out to be 6%). Statement II only gives the maturity amount without specifying the time period, so it's redundant. Statements I and III together are sufficient to find the rate.

Multiple choice

An amount will become 8 times of itself in 3 years with compound interest. Then in how much time it will become 16 times of itself?

  1. 8 years

  2. 4 years

  3. 6 years

  4. 12 years

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

If amount becomes 8 times in 3 years with compound interest, then (1+r)³ = 8, giving 1+r = 2, so r = 100%. To become 16 times, we need (1+r)ᵗ = 16, meaning 2ᵗ = 16, so t = 4 years. At 100% compound interest, the amount doubles every year.

Multiple choice

The simple interest on a certain sum for 2 years at a certain rate of interest is Rs.5000 and compound interest on the same sum, same time and same rate of interest is Rs.5050. Then find the ratio between CI for 2 years and CI for 3 years? ब्याज की एक निश्चित दर पर 2 साल के लिए एक निश्चित राशि पर साधारण ब्याज 5000 रु है और उसी राशि पर चक्रवृद्धि ब्याज, उसी समय और ब्याज की समान दर पर 5050 रु है। फिर 2 साल के लिए चक्रवृद्धि ब्याज और 3 साल के लिए चक्रवृद्धि ब्याज के बीच का अनुपात ज्ञात करें?

  1. 500:7650

  2. 505:7651

  3. 500:7645

  4. 500:7641

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

CI for 2 years = 5050, SI for 2 years = 5000. Difference = 50 is interest on first year's interest. First year interest = 5000/2 = 2500. So 2500 × R/100 = 50, giving R = 10%. CI for 3 years = P(1.1³ - 1) = 5000(0.331) = 1655. Ratio = 5050:7651 = 505:7651 (simplified). This ratio is exactly correct.

Multiple choice

Aman lent Rs 21600 to Sangram for 3 years and Rs 15000 to Pramod for 2 years on simple interest at the same rate of interest and received Rs 2844 in all from both of them as interest. The rate of interest per annum is: अमन ने 3 साल के लिए संग्राम को 21600 रुपये और प्रमोद को 15000 रुपये ब्याज के लिए समान दर पर 2 साल के लिए उधार दिए और ब्याज के रूप में दोनों से 2844 रुपये प्राप्त किए। प्रति वर्ष ब्याज की दर है:

  1. 3.5%

  2. 4%

  3. 3%

  4. 4.5%

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rate = R%. SI from Sangram = (21600 × 3 × R)/100 = 648R. SI from Pramod = (15000 × 2 × R)/100 = 300R. Total interest = 648R + 300R = 948R = 2844. Solving: R = 2844/948 = 3%. Option C is correct.