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

The difference between the interests earned when Rs. P is invested for four years in a scheme offering 9% p.a. Simple interest and when the same sum (Rs P) is invested for two years in another scheme offering 12% p.a. Compound interest, is Rs 528. What is the value of P? जब P रु को 9% साधारण ब्याज देने वाली स्कीम में चार साल के लिए निवेश किया जाता है तथा जब 12% प्रति वर्ष चक्रवृधि ब्याज देने वाली स्कीम में उसी धनराशी (P रु) को दो साल के लिए निवेश किया जाता है तो मिलने वाले ब्याज के बीच का अंतर 528 रु होता है । P का मान क्या है?

  1. 4000

  2. 5000

  3. 4500

  4. 3500

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

For simple interest: SI = P×4×9/100 = 36P/100 = 0.36P. For compound interest at 12% for 2 years: Amount = P(1 + 12/100)² = P(1.12)² = 1.2544P, so CI = 0.2544P. Difference = 0.36P - 0.2544P = 0.1056P. Given 0.1056P = 528, so P = 528/0.1056 = 5280000/1056 = 5000.

Multiple choice

At what percentage rate will the amount of Rs 40000 become Rs 44100 in two years where the interest is compounded annually? 40000 रु की धनराशि किस प्रतिशत दर पर दो वर्षों में 44100 रु हो जाएगी जहाँ ब्याज वार्षिक रूप से चक्रवृद्धि किया जाता है?

  1. 2

  2. 5

  3. 4

  4. 7.5

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

Using compound interest formula A = P(1 + r/100)^t, we substitute 44100 = 40000(1 + r/100)^2. This gives 1.1025 = (1 + r/100)^2, so 1 + r/100 = 1.05 and r = 5%. Verification: 40000 × 1.05 = 42000 after year 1, then 42000 × 1.05 = 44100 after year 2.

Multiple choice

CI on a sum for 3 years at 16.67% rate of interest is Rs. 1587.5. Find the sum. 3 वर्षों का 16.67% ब्याज दर पर चक्रवृद्धि ब्याज 1587.5 रुपये है। मूलधन ज्ञात कीजिए।

  1. 3500

  2. 2700

  3. 2550

  4. 3000

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

16.67% = 1/6. Using CI formula: Amount = P(1 + 1/6)^3 = P(7/6)^3 = P(343/216). CI = P(343/216 - 216/216) = P(127/216). Given CI = 1587.5. So P(127/216) = 1587.5. P = 1587.5 × 216/127 = 2700. Check: 2700/216 = 12.5, 12.5 × 127 = 1587.5. Correct.

Multiple choice

Mahi borrowed a certain sum of money at simple interest for 4 years at 11 % per annum and he pays Rs 44 lakhs as interest . Find the compound interest for same amount at 12.5 % per annum for 2 years ? माही ने 4 साल के लिए साधारण ब्याज पर 11% प्रति वर्ष की दर से एक निश्चित राशि उधार ली और वह ब्याज के रूप में 44 लाख रुपये का भुगतान करता है। 2 वर्ष के लिए प्रति वर्ष 12.5% की राशि पर चक्रवृद्धि ब्याज ज्ञात कीजिये ?

  1. 3256250 Rs 3256250 रुपये

  2. 2656250 Rs 2656250 रुपये

  3. 4000000 Rs 4000000 रुपये

  4. 285620 Rs 285620 रुपये

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

First find the principal: SI = P×R×T gives 44,00,000 = P×0.11×4, so P = 1,00,00,000. For compound interest at 12.5% for 2 years: Year 1 interest = 1,00,00,000×0.125 = 12,50,000; Year 2 interest = (1,00,00,000+12,50,000)×0.125 = 14,06,250. Total CI = 12,50,000+14,06,250 = 26,56,250.

Multiple choice

The C.I. after 3 year on certain sum Rs. 136.5 more than the C.I. of Ist year if rate of compound interest is 1623%1623% then find the sum of money ? किसी धन पर तीन वर्षों के बाद चक्रवृद्धि ब्याज, एक वर्ष के चक्रवृद्धि ब्याज से 136.5 रूपये अधिक है। यदि चक्रवृद्धि ब्याज की दर 1623%1623% है तो मूलधन ज्ञात कीजिए।

  1. 356

  2. 324

  3. 376

  4. 249

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

Let principal be P. CI for 1st year = P × r/100. CI for 3 years = P[(1 + r/100)^3 - 1]. The difference CI(3yr) - CI(1yr) = 136.5. At r = 50/3%, this gives P = 324. (CI1st yr = 54, CI 3yrs = 190.5, difference = 136.5)

Multiple choice

If any amount doubles itself in 5 years at the interest rate compounded annually then in how many years will it become eight times ? यदि कोई धनराशि चक्रवृद्धि ब्याज पर 5 वर्षों में दोगुनी हो जाती है, तो वह धनराशि कितने वर्षों में आठ गुनी हो जायेगी?

  1. 18 years 18 वर्ष

  2. 21 years 21 वर्ष

  3. 24 years 24 वर्ष

  4. 15 years 15 वर्ष

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

If amount doubles in 5 years, then 2^n = 8 gives n = 3. So 3 doubling periods needed. Total time = 3 × 5 = 15 years for amount to become 8 times itself (since 2³ = 8).

Multiple choice

Rajan invest money in 3 different scheme for 6 years, 10 years and 12 years at the rate 10%, 12% and 15% SI respectively at the completion of each scheme he gets the same interest. Then find the ratio of his investment? राजन ने तीन स्कीमों में 6 वर्ष, 10 वर्ष और 12 वर्ष के लिए क्रमशः 10%, 12% और 15% की दर से धन निवेश किया, प्रत्येक स्कीम के अंत में उसको बराबर ब्याज प्राप्त हुआ| तो उसके द्वारा निवेश का अनुपात ज्ञात करें?

  1. 6 : 3 : 2

  2. 6 : 2 : 3

  3. 3 : 6 : 2

  4. 2 : 3 : 6

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

For equal simple interest: P1×6×10% = P2×10×12% = P3×12×15%. Simplifying: P1×60 = P2×120 = P3×180. Dividing by 60: P1×1 = P2×2 = P3×3. Taking LCM 6: Ratio is 6:3:2. Let investments be 6x, 3x, 2x - check: 6x×60 = 360x, 3x×120 = 360x, 2x×180 = 360x.

Multiple choice

A bank offers 10% compound interest per four months. A customer deposits Rs 5000 each on 1st January, on 1st April and on 1st August of a year. At the end of the year, find the amount he would have gained by means of interest? एक बैंक प्रति चार माह 10% चक्रवृद्धि ब्याज की पेशकश करता है। एक ग्राहक एक वर्ष मे 1 जनवरी, 1 अप्रैल और 1 अगस्त को 5000 रुपये जमा करता है। वर्ष के अंत मे ब्याज के माध्यम से उसे कितनी राशि का लाभ होता है?

  1. Rs.1050 1050 रुपये

  2. Rs.3205 3205 रुपये

  3. Rs.5000 5000 रुपये

  4. Rs.2500 2500 रुपये

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

10% CI per 4 months means rates: 10% for 4 months, 21% for 8 months (1.1²-1), 33.1% for 12 months (1.1³-1). Deposits: Jan 1 (3 periods): 5000 × 1.331 = 6655. Apr 1 (2 periods): 5000 × 1.21 = 6050. Aug 1 (1 period): 5000 × 1.1 = 5500. Total maturity = 6655 + 6050 + 5500 = 18205. Principal = 15000. Interest = 18205 - 15000 = 3205.

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?

  1. Rs. 600

  2. Rs. 100

  3. Rs. 80

  4. Rs. 120

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

Let the first part be x at 8% and second part be (3500-x) at 6%. For equal interests: 0.08x = 0.06(3500-x), which gives x = 1500. So first part is Rs 1500 at 8%, second part is Rs 2000 at 6%. Interest on each = 1500 × 0.08 = Rs 120 per year. The key is setting up the equation from the equal interest condition.

Multiple choice

If the compound interest on a certain sum for two years at 12(1/2) % p.a. is 4080, the simple interest on the same sum at the same rate of interest for the same period of time is

  1. Rs.3200

  2. Rs.3600

  3. Rs.3680

  4. Rs.3840
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the compound interest formula: CI = P[(1 + r/100)^n - 1]. At 12.5% for 2 years: 4080 = P[(1.125)^2 - 1] = P[1.265625 - 1] = P(0.265625). Therefore P = 4080/0.265625 = Rs. 15,360. Simple interest = P × R × T / 100 = 15360 × 12.5 × 2 / 100 = 15360 × 0.25 = Rs. 3840. Option D matches this calculation.

Multiple choice

The simple interest accrued on an amount of Rs. 22500 at the end of four years is Rs.5625. What would be the approximate compound interest accrued on the same amount at the same rate after two years? (in Rs.)

  1. 2450

  2. 2630

  3. 2900

  4. 3155

  5. 2732
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest formula: SI = P×R×T/100. Substituting: 5625 = 22500 × R × 4 / 100, giving 562500 = 90000R, so R = 6.25%. Compound Interest for 2 years: Amount = 22500 × (1 + 6.25/100)² = 22500 × 1.0625² ≈ 22500 × 1.1289 ≈ 25400. CI = 25400 - 22500 = 2900 (approximately). Option C matches.

Multiple choice

Find the compound interest on a sum of Rs. 3072 invested in a bank at a compound interest of 6.25%compounded annually for a time period of 2 years and 8 months वार्षिक आधार पर नियोजित 6.25% वार्षिक चक्रवृद्धि ब्याज की दर से एक बैंक में निवेशित रू. 3072 की धनराशि पर 2 वर्ष तथा 8 माह चक्रवृद्धि ब्याज ज्ञात कीजिए।

  1. 540.5

  2. 640.5

  3. 440.5

  4. 390.5

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

Principal = 3072, Rate = 6.25% = 1/16. Time = 2 years 8 months = 2 + 8/12 = 2 + 2/3 years. CI for 2 years = 3072 * [(1 + 1/16)² - 1] = 3072 * [(17/16)² - 1] = 3072 * [289/256 - 1] = 3072 * 33/256 = 396. For remaining 8 months = 2/3 years: CI = (3072 + 396) * (1/16) * (2/3) = 3468/24 = 144.5. Total CI = 396 + 144.5 = 540.5.

Multiple choice

Rahim deposit a sum of rupees 3000 for 5 year. If the rate of simple interest is 4% pa. Find the total interest after 5 year.
  1. $600$
  2. $500$
  3. $700$
  4. $None of these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use Simple Interest = PRT/100. Principal P = 3000, Rate R = 4%, Time T = 5 years. SI = 3000 × 4 × 5 ÷ 100 = 600. This is direct application of the SI formula. Option B (500) would be the result if time was 4 years, and option C (700) is not obtainable from the given data.