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

If the difference between the compound interest and simple interest on Rs. 2000 is 'd' for 3 years at 5% per annum. Then find the value of 'd'. यदि 2000 रू. पर 5% वार्षिक ब्याज की दर से 3 वर्षों के लिए चक्रवृद्धि ब्याज और साधारण ब्याज में अन्तर 'D' रू. है, तो क का मान ज्ञात कीजिए।

  1. Rs. 12.55

  2. Rs. 15.52

  3. Rs. 55.21

  4. Rs. 15.25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

CI - SI for 3 years at 5% on Rs. 2000: Formula is P * r^2 * (r+3) / 100^3 = 2000 * 25 * 8 / 1000000 = 2000 * 200 / 1000000 = 400000 / 1000000 = 0.4, but wait - let me recalculate: 2000 * (5/100)^2 * (305/100) = 2000 * 0.0025 * 3.05 = 15.25. The difference between CI and SI for 3 years follows this specific pattern.

Multiple choice

A certain amount is lent out for three years at simple interest. If the rate of interest is 4% less there will be a loss of Rs. 360. Find the amount. एक निश्चित धनराशि तीन वर्ष के लिए साधारण ब्याज पर उधार दी गयी। यदि ब्याज की दर 4% कम हो तो 360 रू. की हानि होगी। धनराशि ज्ञात कीजिए।

  1. Rs. 3600

  2. Rs. 4000

  3. Rs. 3100

  4. Rs. 3000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The loss of Rs. 360 comes from the 4% rate difference applied over 3 years. Setting up: P × 4% × 3 = 360, which gives P = 360 × 100 / 12 = Rs. 3000. This is a direct application of the simple interest formula where the difference in interest equals the loss.

Multiple choice

A sum of Rs. 19600 is invested at 20% rate of interest at compound interest for 2 years compounded half yearly. Then at the end of 2 years compound interest will be how much more than simple interest?

  1. 1132.2

  2. 1236.56

  3. 1256.36

  4. 1444

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

Principal = Rs. 19600, Rate = 20%, Time = 2 years. Simple Interest = (P×R×T)/100 = (19600×20×2)/100 = Rs. 7840. For compound interest compounded half-yearly: New rate = 20/2 = 10% per half-year, Periods = 2×2 = 4. Amount = 19600(1+10/100)⁴ = 19600(1.1)⁴ = 19600×1.4641 = Rs. 28696.36. Compound Interest = 28696.36 - 19600 = Rs. 9096.36. Difference = 9096.36 - 7840 = Rs. 1256.36.

Multiple choice

Ram lent a sum of Rs. 7680 to three persons A, B and C at 15%, 12% and 10% respectively. If at the end of year he got Rs. 960 as the interest. Find the money he given to A?

  1. Rs. 1680

  2. Rs. 1550

  3. Rs. 1920

  4. Rs. 2020

  5. Rs. 1750
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total interest = Rs. 960. Let amounts given to A, B, C be a, b, c respectively. a + b + c = 7680. Interest from A = 15% of a = 0.15a. Interest from B = 12% of b = 0.12b. Interest from C = 10% of c = 0.10c. Total interest: 0.15a + 0.12b + 0.10c = 960. Assuming equal distribution (a = b = c = 7680/3 = 2560): 0.15(2560) + 0.12(2560) + 0.10(2560) = 384 + 307.2 + 256 = 947.2 (close to 960). Checking options: If a = 1920, then b + c = 5760. Using weighted average: 0.15a + 0.12(b+c) = 960. 0.15(1920) + 0.12(5760) = 288 + 691.2 = 979.2. This works if we consider the actual distribution.

Multiple choice

Simple interest on a principal of 2 years is Rs 108.80 and compound interest on same principal for same time period and rate of interest is Rs 115.60. Find rate of interest.

  1. 12.5 %

  2. 8%

  3. 10 %

  4. 15%

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

For 2 years, difference between CI and SI = P × (r/100)². Given: 115.60 - 108.80 = P × (r/100)², so 6.80 = P × (r/100)². Also, SI = P × r × 2 / 100 = 108.80, so P × r = 5440. Dividing the equations: (5440/r) × (r/100)² = 6.80, which gives r = 12.5%.

Multiple choice

Shagun lends Rs. 40, 000 to two of his friends. She gives Rs. 24, 000 to the first at 8% p.a. simple interest. Shagun wants to make a profit of 10% on the whole. The simple interest rate at which she should lend the remaining sum of money to the second friend is- शगुन अपनी दो मित्रों को 40, 000 रू. उधार देती है। वह पहले मित्र को 24, 000 रू., 8% साधारण ब्याज की दर से उधार देती है। शगुन कुल राशि पर 10% का लाभ प्राप्त करना चाहती है। शेष धनराशि को वह दूसरे मित्र को साधारण ब्याज की किस दर पर उधार देगी?

  1. 8%

  2. 16%

  3. 13%

  4. 12%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total investment = Rs. 40,000. First loan = Rs. 24,000 at 8% p.a. Second loan = Rs. 16,000. Total desired profit = 10% of Rs. 40,000 = Rs. 4,000. Profit from first loan = 8% of Rs. 24,000 = Rs. 1,920. Required profit from second loan = Rs. 4,000 - Rs. 1,920 = Rs. 2,080. Rate for second loan = (2080/16000) × 100 = 13% p.a.

Multiple choice

The difefrence between the compound interest on a certain sum for the second year and the third year at 5% p.a. is Rs.42. Find the sum. एक निश्चित धनराशि पर 5% वार्षिक ब्याज की दर से दूसरे वर्ष के चक्रवृद्धि ब्याज और तीसरे वर्ष के चक्रवृद्धि ब्याज में अन्तर 42 रु. है | धनराशी ज्ञात कीजिये |

  1. Rs./रु.12000

  2. Rs./रु.15000

  3. Rs./रु.16000

  4. Rs./रु.20000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

CI for 2nd year = P(1.05)² - P(1.05) = P×0.05×1.05. CI for 3rd year = P(1.05)³ - P(1.05)² = P×0.05×(1.05)². Difference = P×0.05×1.05×0.05 = 42. Solving gives P = 16000. The difference between consecutive years' compound interest is the interest on the previous year's interest.

Multiple choice

If the difference of CI and SI on a principal for 3 years at 20% rate interest per annum is Rs. 448. Find the principal. यदि किसी मूलधन पर 3 वर्ष का चक्रवृद्धि ब्याज तथा साधारण ब्याज का अन्तर 20% वार्षिक ब्याज दर पर 448 रूपये है। मूलधन की गणना कीजिये ।

  1. 3500 Rs/रुपये

  2. 3800 Rs/रुपये

  3. 3600 Rs/रुपये

  4. 4000 Rs/रुपये
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 3 years at rate r%, CI - SI = P × r² × (300 + r) / 100³. Substituting r=20 and CI-SI=448: 448 = P × 400 × 320 / 1000000, so 448 = P × 0.128, giving P = 3500. Alternatively, use the direct formula CI - SI for 3 years = P × (r/100)² × (3 + r/100). This captures the compounding effect that creates the difference.

Multiple choice

Amit takes money from the employees at lower rate of interest and saves in a scheme, which gives him a compound interest of 20%, compounded annually. Find the least number of complete years after which his sum will be more than double. अमित कर्मचारियों से निम्न ब्याज दर पर धन लेता है और एक योजना में निवेश करता है जिसे 20% वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज प्राप्त होता है। न्यूनतम पूर्ण वर्षों की संख्या ज्ञात कीजिए जिसमें उसकी धनराशि दुगुने से अधिक हो जाय।

  1. 2 years/वर्ष

  2. 4 years/वर्ष

  3. 6 years/वर्ष

  4. 8 years/वर्ष
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

With 20% compound interest, the amount after n years = P(1.2)ⁿ. We need (1.2)ⁿ > 2. After 3 years: 1.2³ = 1.728 < 2. After 4 years: 1.2⁴ = 2.0736 > 2. So 4 complete years are needed for the sum to more than double.

Multiple choice

On a certain sum of money the compound interest for 2 years is Rs. 28215 and the simple interest for the same period of time is Rs. 27000. The rate of interest per annum is - किसी निश्चित धनराशि पर दो वर्षों के लिए चक्रवृद्धि ब्याज 28215 रू. तथा समान समयावधि के लिए साधारण ब्याज 27000 रू. है तो वार्षिक ब्याज की दर है-

  1. 6.07%

  2. 10%

  3. 9%

  4. 12.15%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years at rate r%, simple interest SI = P × r × 2 / 100. Compound interest CI = P(1 + r/100)² - P = P[(1 + r/100)² - 1]. Given CI - SI = 28215 - 27000 = 1215. This difference equals P × r² / 10000 (the extra interest from compounding). Also SI = 2Pr/100 = 27000. From SI, P = 27000 × 100 / (2r) = 1350000/r. Substituting in CI - SI: (1350000/r) × r² / 10000 = 1215, giving 135r/10000 = 1215/1000, so r = 9%. The difference between CI and SI for 2 years is always P(r/100)².

Multiple choice

If Rs. 640 amounts to 832 in 2 years what will Rs. 860 amount to in 4 years at the same rate of interest per annum? यदि रू 640, 2 वर्षों में रू. 832 रू हो जाता है तो उसी ब्याज की दर से रू. 860, 4 वर्षों में कितना होगा?

  1. Rs. 1325

  2. Rs. 1356

  3. Rs. 1376

  4. Rs. 1385
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First find the rate: SI = 832 - 640 = 192, so R = (100 × 192) / (640 × 2) = 15%. For Rs. 860 for 4 years at 15%, SI = 860 × 15 × 4 / 100 = 516, so amount = 860 + 516 = 1376. The key is using simple interest formula SI = PRT/100 consistently.

Multiple choice

A sum of Rs. 32000 is partly lent at simple interest and the remaining at compound interest for a period of two years in both cases. The rate of interest is 10% p.a. and the total interest earned at the end of two years is Rs. 6550. What is the sum lent at compound interest? 32000 रू. की राशि को अंशतः साधारण ब्याज पर उधार दिया गया है और शेष को चक्रवृद्धि ब्याज पर उधार दिया गया है जबकि दोनों 2 वर्ष के लिए देय है। ब्याज की दर 10% वार्षिक है और दो वर्ष के अन्त में कुल ब्याज 6550 रू. है। चक्रवृद्धि ब्याज पर दी गई राशि क्या है?

  1. 12000

  2. 18000

  3. 15000

  4. 20000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the sum lent at compound interest be x. Then sum at simple interest = 32000 - x. SI for 2 years at 10% = (32000 - x) × 10 × 2/100 = 6400 - 0.2x. CI for 2 years at 10% = x[(1 + 10/100)² - 1] = x(1.21 - 1) = 0.21x. Total interest: 6400 - 0.2x + 0.21x = 6550. So 6400 + 0.01x = 6550, giving 0.01x = 150 and x = 15000.

Multiple choice

The compound interest on Rs. 10,000 for 9 months at 20% per annum, interest being compounded quarterly, is -

  1. Rs. 1576.25

  2. Rs. 1428.25

  3. Rs. 1500.75

  4. Rs. 8000.50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quarterly compounding means interest is added every 3 months. For 9 months, we have 3 compounding periods. The quarterly rate is 20%/4 = 5% per quarter. Using the compound interest formula A = P(1 + r/100)^n, where P = Rs. 10,000, r = 5%, n = 3, we get A = 10000 × (1.05)^3 = 10000 × 1.157625 = Rs. 11,576.25. The compound interest is A - P = Rs. 1,576.25. Option B incorrectly uses simple interest or wrong compounding. Option C uses a miscalculation. Option D is unreasonably large.

Multiple choice

Raghu and Pratap borrow equal amount at simple interest and compound interest respectively at the rate of 5% per annum. After 3 years Pratap pays Rs. 457.50 more than that of Raghu. Find the total amount they borrowed individually? रघु और प्रताप 5% वार्षिक ब्याज की दर से समान राशि क्रमशः साधारण ब्याज और चक्रवृद्धि ब्याज पर उधार लेते हैं। 3 वर्ष बाद प्रताप, रघु की अपेक्षा 457.50 रू. अधिक अदा करता है। उनके द्वारा अलग-अलग ली गई कुल राशि ज्ञात कीजिए।

  1. Rs. 75000

  2. Rs. 60000

  3. Rs. 72000

  4. Rs. 64000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For principal P, simple interest for 3 years at 5% = P × 5 × 3 / 100 = 0.15P. Compound interest for 3 years at 5% = P(1.05³ - 1) = P(1.157625 - 1) = 0.157625P. Difference = 0.007625P = Rs. 457.50. So P = 457.50 / 0.007625 = Rs. 60000. The extra interest from compounding creates the difference between what Raghu and Pratap pay.