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

Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3% it would amount to - 800 रू.की धनराशि सा. ब्याज की दर से 3 वर्षो में 920 रू. हो जाती है । यदि ब्याज की दर 3% की वृद्धि होती है तो धनराशि होगी?

  1. Rs.1056

  2. Rs.1112

  3. Rs.1182

  4. Rs.992
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Principal = Rs. 800, Amount = Rs. 920, Time = 3 years. Simple Interest = 920 - 800 = Rs. 120. Rate = (100 × SI) / (P × T) = (100 × 120) / (800 × 3) = 5% per annum. New rate = 5% + 3% = 8%. New SI = (800 × 8 × 3) / 100 = Rs. 192. New Amount = 800 + 192 = Rs. 992.

Multiple choice

The difference between compound interest and simple interest at the same rate on Rs. 5000 for 2 years is Rs.72. The rate of interest per annum is - 5000 रू. का दो वर्षो में चक्रवृद्धि ब्याज और साधारण ब्याज एक ही ब्याज दर पर 72 रू. हो तो ब्याज की दर प्रति वर्ष है -

  1. 6%

  2. 8%

  3. 10%

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

For 2 years, CI - SI = P(r/100)². Here: 72 = 5000 × r²/10000. Solving: r² = 72 × 2 = 144, so r = 12%. The difference between compound and simple interest for 2 years comes from the interest on interest, which grows with the square of the rate.

Multiple choice

Find the correct relationship between the given quantities: Quantity I: The difference between the rate of CI and rate of depreciation if a person Aakash has a sum of INR 2500 which after 3 years at compound interest @20% p.a. becomes a certain amount that is equal to the amount that is the result of 3-year compounded depreciation from INR 8437.5. Quantity II: 5%.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For compound interest at 20% for 3 years on Rs. 2500: Amount = 2500(1.2)³ = 2500(1.728) = Rs. 4320. For depreciation, let the rate be r%. Then 8437.5(1-r/100)³ = 4320. Solving: (1-r/100)³ = 4320/8437.5 = 0.512. Taking cube root: 1-r/100 = 0.8, so r = 20%. Therefore, the depreciation rate is also 20%. The difference between CI rate (20%) and depreciation rate (20%) is 0%. Since 0% < 5%, Quantity II > Quantity I.

Multiple choice

Find the correct relationship between the given quantities: Quantity I: Compound interest 2 years from now, if 2 years ago, a sum of Rs.2000 was compounded annually, amounts to Rs. 2420 at present. Quantity II: 92.82% of Simple interest, calculated on a sum of Rs.2000 @ 5% rate of interest, calculated for a period of decade or more.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: 2000 grows to 2420 in 2 years at r% compounded annually. 2000(1+r/100)² = 2420, so (1+r/100) = 1.1, giving r = 10%. CI for next 2 years = 2420(1.1)² - 2420 = 292.82 - 2420 = 292.82. Quantity II: SI on Rs 2000 at 5% for 10 years = 2000×5×10/100 = 1000. 92.82% of 1000 = 928.2. 928.2 > 292.82.

Multiple choice

A person invested P on compound interest at the rate of 10\% for 2 years, and invested (P+200) at the rate of 14\% simple interest for 4 years. The total interest obtained is 6965. Find the total amount (in rupees) invested by the person.

  1. 8900

  2. 18000

  3. 17500

  4. 17800

  5. 15800
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First investment: P at 10% CI for 2 years. Amount = P(1.1)^2 = 1.21P. Interest = 0.21P. Second: (P + 200) at 14% SI for 4 years. Interest = (P + 200) * 0.14 * 4 = 0.56(P + 200) = 0.56P + 112. Total interest = 0.21P + 0.56P + 112 = 0.77P + 112 = 6965. So 0.77P = 6853, P = 6853/0.77 = 8900. Total amount invested = P + (P + 200) = 2P + 200 = 17800 + 200 = 18000. The answer represents the total principal invested across both schemes.

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?

  1. Rs.1050

  2. Rs.3205

  3. Rs.5000

  4. Rs.2500

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

10% interest per 4 months means quarterly compounding at 10%. Jan deposit: compounds 3 times (Apr, Aug, Dec). Apr deposit: compounds 2 times (Aug, Dec). Aug deposit: compounds 1 time (Dec). Interest = 5000×1.1³ + 5000×1.1² + 5000×1.1 - 15000. This equals 5000×(1.331 + 1.21 + 1.1) - 15000 = 5000×3.641 - 15000 = 18205 - 15000 = Rs.3205.

Multiple choice

Ramesh invested an amount of Rs.12000 at the simple interest rate of 10% per annum and another amount at the simple rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 14% per annum. Find the total amount invested. रमेश ने 12000 रू. को 10% वार्षिक साधारण ब्याज की दर पर निवेश किया और कुछ अन्य धनराशि को 20% वार्षिक साधारण ब्याज की दर पर निवेश किया। एक वर्ष के अन्त में कुल धनराशि पर कुल ब्याज 14% वार्षिक की दर के बराबर हुआ निवेश की कुल राशि कितनी थी?

  1. Rs.25000

  2. Rs.21000

  3. Rs.20800

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

Let second amount be x. Total interest = 12000×0.10 + x×0.20 = 1200 + 0.2x. Total investment = 12000 + x. Average rate = (1200 + 0.2x)/(12000 + x) = 0.14. Solving: 1200 + 0.2x = 1680 + 0.14x, giving 0.06x = 480, so x = 8000. Total = 12000 + 8000 = 20000.

Multiple choice

The compound interest on any sum at the rate of 5% for two years is Rs.553.50. Find the sum. किसी राशि पर 5% प्रति वर्ष की दर से 2 वर्ष का चक्रवृद्धि ब्याज 553.50 रू. है। मूल धनराशि क्या होगी?

  1. Rs.5400

  2. Rs.5200

  3. Rs.5000

  4. Rs.4900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using CI formula: CI = P(1 + r/100)² - P = P[(1.05)² - 1] = P(1.1025 - 1) = P(0.1025) = 553.50. So P = 553.50/0.1025 = 5400. Compound interest for 2 years at 5% gives 10.25% total interest.

Multiple choice

Anu invested an amount of Rs.6950 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs.1754, what was the amount invested in scheme B? अनु ने 6950 रुपये की राशि को दो अलग-अलग योजनाओं A और B में क्रमशः 14% और 11% वार्षिक साधारण ब्याज की दर पर निवेश किया। यदि 2 वर्ष में अर्जित साधारण ब्याज की कुल राशि 1754 रुपये है, तो योजना B में निवेश की गई राशि क्या थी?

  1. Rs.3200

  2. Rs.3250

  3. Rs.3600

  4. Rs.3750
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let amount in scheme B be x. Then amount in A is 6950 - x. Total simple interest = (6950 - x) × 14 × 2/100 + x × 11 × 2/100 = 1754. Solving: 194600 - 28x + 22x = 175400, so 6x = 19200 and x = 3200. The correct answer is Rs.3200.

Multiple choice

Amit deposited two parts of a sum of Rs. 25000 in different banks at the rates of 15% per annum and 18% per annum respectively. In one year he got Rs.4050 as the total interest. What was the amount deposited at the rate of 18% per annum? अमित ने 25000 रू. के दो भाग अलग-अलग बैकों में 15% और 18% वार्षिक की दर से जमा कराये। यदि एक वर्ष में उसको 4050 रू. का ब्याज मिला तो 18% ब्याज दर पर कितना धन लगाया गया था?

  1. Rs./रू.10000

  2. Rs./रू.12000

  3. Rs./रू.15000

  4. Rs./रू.18000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let amount at 18% be x. Then 0.15(25000-x) + 0.18x = 4050. 3750 - 0.15x + 0.18x = 4050. 0.03x = 300. x = 10000. Verify: 15000 at 15% gives 2250, 10000 at 18% gives 1800, total = 4050. Correct.

Multiple choice

Anupam invests Rs.28575 in a bond which gives interest at 3% per annum during the first year, 5% during the second year and 8% during the third year. How much amount does he get at the end of the third year? अनुपम 28575 रू. ऐसे बांड में निवेश करता है जो पहले वर्ष 3% प्रतिवर्ष की दर से, दूसरे वर्ष 5% प्रतिवर्ष की दर से और तीसरे वर्ष 8% प्रतिवर्ष की दर से ब्याज देते हैं। तीसरे वर्ष के अंत में उसे कितनी धनराशि मिलेगी?

  1. Rs. /रू. 33376.2

  2. Rs. /रू. 33151.8

  3. Rs. /रू. 36181.5

  4. Rs. /रू. 39076.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Compound interest with varying rates: Year 1: 28575 × 1.03 = 29432.25. Year 2: 29432.25 × 1.05 = 30903.86. Year 3: 30903.86 × 1.08 = 33376.17 (rounds to 33376.2). Option B is simple interest calculation, C and D are arithmetic errors.

Multiple choice

On what sum of money will the difference between simple interest and compound interest for 3 years at 5% per annum be equal to Rs.951.6? किस राशि पर 3 वर्षों के साधारण ब्याज और चक्रवृद्धि ब्याज में अन्तर 5 % वार्षिक ब्याज की दर से रु.951.6 है ?

  1. Rs.126100

  2. Rs.124800

  3. Rs.126000

  4. Rs.125500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CI - SI difference for 3 years at rate r is P × r² × (3+r)/100². Here P × 25 × (3+5)/100² = P × 200/10000 = 0.007625P. Setting 0.007625P = 951.6 gives P = 951.6/0.007625 = 124800.

Multiple choice

A sum become Rs. 3240 in 3 year at certain rate of compound interest and same sum of money become Rs. 3888 in 4 year at same rate of compound interest find the principle? एक धनराशि चक्रवृद्धि ब्याज की दर से 3 वर्षो में 3240 रू. हो जाती है। वही धनराशि 4 वर्षों में उसी ब्याज की दर से 3888 रू. हो जाती है। मूलधन ज्ञात कीजिए।

  1. 1275

  2. 1800

  3. 2820

  4. 1875
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ratio of amounts after consecutive years gives the rate: 3888/3240 = 1.2, so 1+r = 1.2, r = 20%. Then P(1.2)^3 = 3240, so P = 3240/1.728 = Rs. 1875.

Multiple choice

If interest is earned Rs 50 in 1 year and 65 rupees in 2 years under compound interest from a sum of money, then what is the rate of interest per annum?

  1. 10%

  2. 30%

  3. 25%

  4. 32%

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

Under compound interest, Year 1 interest = Pr, Year 2 total interest = P(1+r)r + Pr = Pr(2+r). Given: Pr = 50 and Pr(2+r) = 65. So 50(2+r) = 65, giving 2+r = 1.3, so r = 0.3 = 30%. Verification: Year 1: 50, Year 2: 50×0.3×1.3 + 50 = 19.5 + 50 = 69.5. But given total is 65, so 50(2+r) = 65 means 2+r = 1.3, r = 30% is correct.

Multiple choice

A sum of Rs.30000 is invested for 18 months at 20% per annum on compound interest. If the interest is compounded half yearly. Then find the how much interest to be paid?

  1. Rs.9930

  2. Rs.9940

  3. Rs.9830

  4. Can't be determined

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

Principal = Rs. 30000, Rate = 20% p.a., Time = 18 months = 1.5 years. Half-yearly compounding means 3 periods at 10% per period. Amount = 30000 × (1.10)^3 = 30000 × 1.331 = Rs. 39930. Interest = 39930 - 30000 = Rs. 9930.