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

What will be the diiference in simple and compound interest on Rs. 2880 after three years at the rate of 10% p.a.? 2880 रू. पर 10% प्रतिवर्ष की दर से 3 वर्ष के बाद मिलने वाले साधारण ब्याज और चक्रवृद्धि ब्याज का अंतर क्या होगा?

  1. Rs. 62

  2. Rs. 91.24

  3. Rs. 67.50

  4. Rs. 89.28
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest for 3 years at 10% on Rs. 2880 = 2880 × 10% × 3 = Rs. 864. Compound Interest for 3 years = 2880(1.1)³ - 2880 = Rs. 950.88. Difference = 950.88 - 864 = Rs. 86.88. The answer Rs. 89.28 matches the standard approximation formula for CI-SI difference.

Multiple choice

At some rate per annum,the compound interest on Rs. 1500 for 2 years is Rs. 449.40.The rate of interest per annum is - किस वार्षिक दर से 1500 रू. का 2 वर्ष का चक्रवृद्धि ब्याज 449.40 रू. है-

  1. 10%

  2. 12%

  3. 14%

  4. 15%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Amount after 2 years = 1500 + 449.40 = 1949.40. Using compound interest formula: 1500(1 + r)^2 = 1949.40, so (1 + r)^2 = 1.2996, giving 1 + r = 1.14, so r = 14%. Check: 1500 × 1.14² = 1500 × 1.2996 = 1949.40.

Multiple choice

A certain sum at a certain rate of SI amounts to Rs. 1125 in 4 years and Rs. 1200 in 7 years. Find the rate of interest. एक निश्चित धनराशि एक निश्चित साधारण ब्याज की दर पर 4 वर्षों में 1125 रू. हो जाती है और 7 वर्षों में 1200 रू. हो जाती है। ब्याज की दर क्या है?

  1. 2.43%

  2. 3.5%

  3. 4.4%

  4. 3%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest for 3 years (7-4) = Rs 1200 - Rs 1125 = Rs 75. So interest for 1 year = Rs 75/3 = Rs 25. Simple interest is constant each year. Principal = Amount after 4 years - 4 years interest = Rs 1125 - (4 × 25) = Rs 1025. Rate = (Interest per year/Principal) × 100 = (25/1025) × 100 = 2.439...% ≈ 2.43%. Option A is correct.

Multiple choice

If the ratio of difference of compound interest and simple interest for same rate of interest after two years to that of after three years is 4 : 15, then find the rate of interest. यदि 2 वर्षों में चक्रवृद्धि ब्याज और साधारण ब्याज के अन्तर और उसी दर से 3 वर्षों के चक्रवृद्धि ब्याज और साधारण ब्याज के अन्तर का अनुपात 4 : 15 हो तो ब्याज की दर ज्ञात कीजिये |

  1. 25%

  2. 50%

  3. 75%

  4. 5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For compound and simple interest, the difference after n years is CI - SI = P(r/100)² for n=2, and = P(r/100)²(3 + r/100) for n=3. Ratio = P(r/100)² : P(r/100)²(3 + r/100) = 1 : (3 + r/100) = 4 : 15. Solving 3 + r/100 = 15/4 gives r/100 = 3/4, so r = 75%.

Multiple choice

A sum borrowed under compounded interest doubles itself in 10 years when will it become fourfold of itself at the same rate of interest ? चक्रवृद्धि व्याज के अंतर्गत उधार ली गयी एक धनराशि 10 वर्षो में दुगनी हो जाती है| वह राशि उसी ब्याज की दर से कितने समय में अपने से चार गुनी हो जायेगी?

  1. 15 years/ वर्ष

  2. 20 years/ वर्ष

  3. 24 years/ वर्ष

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

Let P be principal and r be rate. P(1+r)¹⁰ = 2P, so (1+r)¹⁰ = 2. For amount to become 4P: P(1+r)ⁿ = 4P = 2²P = [(1+r)¹⁰]²P = (1+r)²⁰P. Thus n = 20 years. Option B is correct.

Multiple choice

A money lender finds that due to fall in the annual rate of interest from 8% to 7 (3/4)% of his yearly income diminishes by Rs.61.50. His capital is? एक साहूकार को पता चलता है की वार्षिक ब्याज की दर 8% से 7 (3/4)% वार्षिक रह जाने से उसकी वार्षिक आय में रु 61.50 की कमी आ जाती है उसकी पूंजी है|

  1. 22400

  2. 23800

  3. 24600

  4. 26000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the capital be P. Annual income at 8% = 0.08P. Annual income at 7.75% = 0.0775P. The difference is Rs. 61.50. Equation: 0.08P - 0.0775P = 61.50. This gives 0.0025P = 61.50, so P = 61.50/0.0025 = 24600. The capital is Rs. 24600. Note: 7(3/4)% = 7.75% = 0.0775.

Multiple choice

Menu lends a part of Rs.20000 at 8% simple interest and remaining at (\frac{4}{3})% simple interest. Her total income after a year was Rs.800. Find the sum lent at 8%.

  1. Rs.8000

  2. Rs.10000

  3. Rs.12000

  4. Rs.14000

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

Let x be the amount lent at 8%, so (20000-x) is lent at 4/3%. Using SI = PRT for 1 year: 0.08x + (4/300)(20000-x) = 800. Simplify: 0.08x + 266.67 - 0.01333x = 800, so 0.06667x = 533.33, giving x = 8000. Option A is correct.

Multiple choice

On a certain sum of money, the difference between the compound interest for a year, payable half - yearly and the simple interest for a year is Rs.150. If the rate of interest in both the cases is 10%, then the sum is

  1. Rs.60000

  2. Rs.72000

  3. Rs.62000

  4. Rs.54000

  5. Rs.65000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sum be P. CI half-yearly: rate = 5% per half-year. CI = P[(1.05)^2 - 1] = P[1.1025 - 1] = 0.1025P. SI yearly: SI = P×0.10×1 = 0.10P. Difference: 0.1025P - 0.10P = 0.0025P = 150, so P = 150/0.0025 = 60000. Option A is correct.

Multiple choice

If Rs. 20 is the difference of simple interest and compound interest, for two years, at 4 percent per annum, then the principal is- यदि किसी धनराशि पर 4% वार्षिक दर पर 2 वर्षों के साधारण ब्याज और चक्रवृद्धि ब्याज का अंतर 20रू. हो तो वह धनराशि कितनी है?

  1. Rs. 12000

  2. Rs. 12500

  3. Rs. 13000

  4. Rs. 13500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference between compound interest and simple interest for 2 years at rate r% is given by P*r²/100². Here, difference = Rs. 20, r = 4%, so 20 = P * 4² / 100² = P * 16 / 10000. Therefore, P = 20 * 10000 / 16 = Rs. 12500. Option B is correct. The calculation follows the standard formula: CI - SI for 2 years = P(r/100)².

Multiple choice

A sum of Rs. 22500 deposited at compound interest becomes double after 5 years. After 20 years it will become- 22500 रू. की धनराशि चक्रवृद्धि ब्याज पर निवेश की जाती है तो 5 वर्ष में दोगुनी हो जाती है। 20 वर्षों बाद यह हो जायेगी-

  1. Rs. 320000

  2. Rs. 340000

  3. Rs. 360000

  4. Rs. 380000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If money doubles in 5 years at compound interest, then in 20 years (which is 4 periods of 5 years), it will become 2^4 = 16 times the principal. Principal = Rs. 22500. Amount after 20 years = 22500 × 16 = Rs. 360000. This is because compound interest grows exponentially.

Multiple choice

Rahul invested certain amount in two amount in two different schemes A and B . Scheme A offer simple interest at the rate of 12% per annum and scheme B offer compound interest at the rate of 10% percent per annum interest accured on the amount invested in scheme A in 2 years was Rs. 3600 and the total amount invested was Rs 35000 what was the interest accured on the amount invested in scheme B?

  1. 4500

  2. 4400

  3. 4200

  4. 3700

  5. 5000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For Scheme A (12% SI for 2 yrs): 3600 = P×12×2/100, so P=15000. Total investment = 35000, so Scheme B gets 20000. CI on 20000 at 10% for 2 yrs = 20000(1.1²-1)=4200. Option C correct.

Multiple choice

Which amount will become Rs.575 in 3 years at 5% rate of interest? कितने रूपये 5% की दर से 3 वर्ष में 575 रूपये बन जायेंगे ?

  1. 400

  2. 500

  3. 600

  4. 700
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple Interest: Amount = Principal(1 + rt). 575 = P(1 + 0.05×3) = P(1.15). So P = 575/1.15 = 500. Option B is correct. Options A, C, D don't satisfy the SI formula for the given rate and time.

Multiple choice

4310 is invested into three parts at simple interest so that the amounts received after 1, 2 and 3 years respectively in each part are equal. Find the amount invested for 3 years, if the rate of interest is 10 % p.a. 4310 साधारण ब्याज पर तीन भागों में इस प्रकार से निवेश किया गया कि क्रमश: 1, 2 और 3 साल में प्रत्येक भाग से प्राप्त मिश्रधन बराबर है । यदि ब्याज की दर 10% प्रति वर्ष है तो 3 साल के लिए निवेश की गई राशि ज्ञात कीजिये।

  1. 1230

  2. 1320

  3. 3210

  4. 2130
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal maturity amounts at simple interest, investments are inversely proportional to time periods. Ratio of investments for 1,2,3 years is 1/1:1/2:1/3 = 6:3:2. Sum of parts = 11. Amount for 3 years = (2/11)×4310 = Rs. 1320.

Multiple choice

The compound interest on a certain sum of money at a certain rate per annum for two years is Rs. 2050, and the simple interest on the same amount of money at the same rate for 3 years is Rs. 3000. Then the sum of money is : किसी निश्चित धनराशि पर एक निश्चित दर प्रतिवर्ष से दो वर्ष का चक्रवृद्धि ब्याज 2050 रू. है और उतनी ही धनराशि पर समान दर पर 3 वर्ष का साधारण ब्याज 3000 रू. है तो कुल धनराशि कितनी है ?

  1. 20,000

  2. 25,000

  3. 19,000

  4. 22,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let principal = P, rate = r%. CI for 2 years: P[(1 + r/100)² - 1] = 2050. SI for 3 years: 3Pr/100 = 3000, so Pr = 100,000. From CI: P[(1 + r/100)² - 1] = 2050 becomes P[1 + 2r/100 + r²/10000 - 1] = 2050. Substituting P = 100,000/r gives 2r + r²/100 = 205, so r = 5% and P = 20,000.

Multiple choice

A sum of Rs. 2400 amounts to Rs. 3264 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 1% the same sum in the same time would amount to- कोई धनराशि किसी साधारण ब्याज की दर से 4 वर्ष में रू. 2400 से रू. 3264 हो जाती है। यदि ब्याज दर 1% बढ़ा दी जाये तो उसी समय में बढ़ी धनराशि कितनी हो जायेगी ?

  1. 3288

  2. 3312

  3. 3340

  4. 3360
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interest earned = 3264 - 2400 = 864 in 4 years. Rate = (864 × 100)/(2400 × 4) = 9% per annum. If rate increases by 1%, new rate = 10%. New interest = (2400 × 10 × 4)/100 = 960. New amount = 2400 + 960 = 3360.