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 simple interest on a sum of money be 20% of the principal in 4 years, then find the rate percent per annum. किसी धनराशि पर 4 सालों का साधारण ब्याज मूलधन का 20 प्रतिशत है तो ब्याज की दर ज्ञात कीजिए।

  1. 8%

  2. 10%

  3. 6%

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

SI = P×R×T/100. Given SI = 20% of P = 0.2P, T = 4 years. So 0.2P = P×R×4/100. Solving: 0.2 = 4R/100, R = 5%. Options A, B, C (8%, 10%, 6%) are incorrect.

Multiple choice

At the certain rate of interest the compound interest of 3 years and simple interest of 5 years for certain sum of money is respectively Rs. 1513.2 and Rs. 2400. Find the rate of interest per annum. किसी निश्चित ब्याज की दर से किसी निश्चित धनराशि का 3 वर्ष का चक्रवृद्धि ब्याज एवं 5 वर्ष का साधारण ब्याज क्रमशः 1513.2 रू. तथा 2400 रू. है तो प्रतिवर्ष ब्याज दर ज्ञात कीजिए।

  1. 10%

  2. 5%

  3. 8%

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

Set up SI formula: P×r×5/100 = 2400, giving P×r = 48000. Testing r=5%, P = 48000/5 = 9600. CI = 9600[(1.05)³-1] = 9600[1.157625-1] = 9600×0.157625 = 1513.2, which matches exactly. The rate is 5%.

Multiple choice

Raman lends 40% of his sum of money at 15% per annum, 50% of rest at 10% per annum and the rest at 18% per annum rate of interest. What would be annual rate of interest, if the interest is calculated on the whole sum? रमण अपनी राशि का 40%, 15% वार्षिक ब्याज की दर से, शेष का 50%, 10% वार्षिक ब्याज की दर से और शेष को 18% वार्षिक ब्याज की दर से देता है | वार्षिक ब्याज की दर क्या है यदि ब्याज को पूरी राशि पर गणित किया जाय ?

  1. 13.4%

  2. 14.33%

  3. 14.4%

  4. 13.33%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total sum be Rs.100. 40% at 15% gives Rs.6 interest. Remaining 60%: 50% of this (30% of total) at 10% gives Rs.3 interest. Rest (30% of total) at 18% gives Rs.5.4 interest. Total interest = 6 + 3 + 5.4 = Rs.14.4 on Rs.100, which is 14.4%. Options A (13.4%), B (14.33%), and D (13.33%) are calculation errors.

Multiple choice

With a given rate of simple interest the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years, with the same rate of interest, the ratio of principal and amount becomes 5 : 7. The rate of interest is एक दी गयी साधारण ब्याज की दर से मूलधन और मिश्रधन का किसी समयावधि के पश्चात अनुपात 4 : 5 हो जाता है | 3 वर्ष बाद, उसी ब्याज की दर से मूलधन और मिश्रधन में अनुपात 5 : 7 हो जाता है | ब्याज की दर है

  1. 4%

  2. 5%

  3. 6%

  4. 7%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Principal:Amount = 4:5 means Interest = 1/4 of Principal. Let rate = r%, time = t years. Then rt/100 = 25 (since 4:5 ratio means 25% interest). After 3 years, ratio 5:7 means Interest = 2/5 = 40%. So r(t+3)/100 = 40. Subtracting: 3r/100 = 15, r = 5%.

Multiple choice

A man borrows some money at 3% simple interest per annum and lends it to somebody at 5% interest to be compunded annually. By this he makes a profit of Rs. 541 at the end of 3 years. The money he borrowed was- एक आदमी ने 3% साधारण वार्षिक ब्याज पर कुछ राशि उधार ली और उसे 5% वार्षिक चक्रवृद्धि ब्याज पर किसी को ऋण पर दे दिया। इस प्रकार उसे 3 वर्ष के अंत में रू. 541 लाभ कमाया। उसके द्वारा उधार ली गयी राशि थी-

  1. Rs. 8,000

  2. Rs. 6,762

  3. Rs. 6,000

  4. Rs. 8,070
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

SI cost for 3 years at 3%: P × 3 × 0.03 = 0.09P. CI earned at 5% for 3 years: P(1.05³ - 1) = 0.157625P. Profit = 0.067625P = 541, giving P = 8000. The difference between compound interest earned and simple interest paid is the profit.

Multiple choice

If the difference between interest received by A and B is Rs. 216 on Rs. 3600 for 3 years. What is the difference in rate of interest ? यदि A और B द्वारा प्राप्त ब्याज का अन्तर 3600 रू. के लिए 3 वर्ष में 216 रू. है तो ब्याज दरों में अन्तर क्या है ?

  1. 1%

  2. 1.5%

  3. 2%

  4. 2.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the rate difference be d%. The interest difference is 3600 × 3 × d/100 = 216. Solving: 108d = 216, so d = 2%. This is a direct application of the simple interest formula.

Multiple choice

A person has left an amount of Rs. 1,20,000 to be divided between his 2 sons aged 14 years and 12 years such that they get equal amounts when each attains 18 years of age at the rate of 5% simple interest per annum. Then what was the share of younger son at present? एक व्यक्ति 1,20,000 रू. अपने दो, 12 वर्ष एवं 14 वर्ष के दो पुत्रों इस प्रकार बाँटता है कि 5 प्रतिशत वार्षिक साधारण ब्याज की दर से दोनों को 18 वर्ष की आयु पर समान धन प्राप्त हो तो छोटे पुत्र की वर्तमान में कितनी राशि है?

  1. 48800

  2. 57600

  3. 62400

  4. 84400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Younger son (12 years) waits 6 years, older son (14 years) waits 4 years. At 18, both get equal amounts: Y(1 + 5×6/100) = O(1 + 5×4/100), so 1.3Y = 1.2O, meaning Y = 12O/13. With Y + O = 1,20,000, we get 25O/13 = 1,20,000, so O = 62,400 and Y = 57,600.

Multiple choice

Find the differnce between the compound interest and simple interest on Rs.40000 at 10% p.a. for 4 years? रु.40000 पर 4 वर्षों में 10% वार्षिक ब्याज की दर से साधारण ब्याज और चक्रवृद्धि ब्याज में अन्तर ज्ञात कीजिये |

  1. Rs./रु.2564

  2. Rs./रु.2562

  3. Rs./रु.2546

  4. Rs./रु.2564.20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

SI = 40000 × 0.10 × 4 = Rs 16000. CI = 40000(1.10)^4 - 40000 = 40000 × 1.4641 - 40000 = Rs 18564 - 40000 = Rs 18564. CI - SI = 18564 - 16000 = Rs 2564. For quick verification: difference between CI and SI for 3 years at 10% is P(R^2)(R+3)%, and it increases each year. The difference grows with time due to the compounding effect on interest.

Multiple choice

Naimish borrows Rs. 40000 from Axix Bank at rate of 7.50% per annum at compund interest. At end of every year he pays Rs. 15000 which consist of interest and a part of a loan repayment. How much more he has to pay at the end of third year to finish his loan.

  1. Rs. 16232.5

  2. Rs. 1232.5

  3. Rs. 1000

  4. Rs. 100

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

Year 1: Principal = Rs. 40,000. Interest at 7.5% = Rs. 3,000. After paying Rs. 15,000, remaining principal = 28,000. Year 2: Interest on Rs. 28,000 at 7.5% = Rs. 2,100. After paying Rs. 15,000, remaining principal = 15,100. Year 3: Interest on Rs. 15,100 at 7.5% = Rs. 1,132.50. Total due = 15,100 + 1,132.50 = Rs. 16,232.50. If he pays the usual Rs. 15,000, the remaining amount to clear the loan = 16,232.50 - 15,000 = Rs. 1,232.50. Key insight: Compound interest is calculated on the outstanding balance each year, and payments first cover interest then reduce principal.

Multiple choice

Find the difference between the compound interest and the simple interest on Rs. 32000 at 10% p.a. for 4 years. 32000 की धनराशि पर 4 वर्ष के लिए 10% वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज और साधारण ब्याज का अन्तर बताइए।

  1. Rs. 2051.20

  2. Rs. 2052.50

  3. Rs. 2025.20

  4. Rs. 2501.20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple Interest = 32000 × 10 × 4/100 = Rs. 12800. Compound Interest = 32000(1.1^4 - 1) = Rs. 14851.20. The difference = CI - SI = 14851.20 - 12800 = Rs. 2051.20, which occurs because compound interest earns interest on the accumulated interest each year.

Multiple choice

A certain sum in certain time becomes Rs.500 at the rate of 8% per annum simple interest and the same sum amounts to Rs.200 at the rate of 2% simple interest in the same duration. Find the time. एक निश्चित धनराशि निश्चित समय में 8% प्रति वर्ष साधारण ब्याज की दर पर 500 रू.हो जाती है और यही धनराशि 2% प्रतिवर्ष साधारण ब्याज की दर पर इसी समय में 200 रू. हो जाती है। समय ज्ञात कीजिए।

  1. 25 years/वर्ष

  2. 30 years/वर्ष

  3. 40 years/वर्ष

  4. 50 years/वर्ष
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For simple interest: Amount = Principal + (Principal × Rate × Time)/100. Let P be principal and T be time. At 8%: 500 = P + (P × 8 × T)/100 = P(1 + 0.08T). At 2%: 200 = P(1 + 0.02T). Dividing the equations gives 500/200 = (1 + 0.08T)/(1 + 0.02T). Solving: 2.5(1 + 0.02T) = 1 + 0.08T, which gives 2.5 + 0.05T = 1 + 0.08T, so 1.5 = 0.03T, and T = 50 years.

Multiple choice

The difference between compound interest for 3 years and simple interest for one year at the rate of 3% on a certain sum of money is Rs. 3136.35/- then find the sum ? किसी निश्चित धन पर 3% दर से 3 वर्षों के चक्रवृद्धि ब्याज और एक वर्ष के साधारण ब्याज का अन्तर रू. 3136.35/- है, तो मूलधन ज्ञात कीजिए।

  1. Rs. 50000

  2. Rs. 45000

  3. Rs. 48000

  4. Rs. 30000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 3 years CI and 1 year SI at 3%, the difference arises from compound effect. CI for 3 years at 3%: P × 1.03³ - P. SI for 1 year at 3%: P × 0.03. Difference = P(1.03³ - 1 - 0.03) = P(1.092727 - 1.03) = P × 0.062727. Given difference = Rs. 3136.35, so P = 3136.35/0.062727 ≈ Rs. 50,000.

Multiple choice

Ramu borrowed Rs.1000 at 8% simple interest and Ravi borrowed Rs.1400 at 5% simple interest. After how much time they will have equal debts? रामू ने रू.1000 को 8% वार्षिक साधारण ब्याज की दर से तथा रवि ने रू.1400 को 5% वार्षिक साधारण ब्याज की दर से उधार लिया । कितने समय बाद दोनों का ऋण बराबर हो जाएगा?

  1. 25 years/वर्ष

  2. 15 years/वर्ष

  3. 40 years/वर्ष

  4. 50 years/वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ramu's debt after t years: 1000 + (1000×8×t)/100 = 1000 + 80t. Ravi's debt: 1400 + (1400×5×t)/100 = 1400 + 70t. Set equal: 1000 + 80t = 1400 + 70t, giving 10t = 400, so t = 40 years.

Multiple choice

If Rs.x was invested at 12% per annum simple interest and a sum of money Rs.y is invested at 10% per annum simple interest. If the sum of the interest on both the sum after 4 years is Rs.480. If the ratio between x and y is 5 : 6, the later sum of money is

  1. Rs.500

  2. Rs.550

  3. Rs.600

  4. Rs.750
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest = Principal × Rate × Time. For Rs.x at 12% for 4 years: SI₁ = x × 0.12 × 4 = 0.48x. For Rs.y at 10% for 4 years: SI₂ = y × 0.10 × 4 = 0.40y. Total interest: 0.48x + 0.40y = 480. Given x:y = 5:6, let x = 5k, y = 6k. Then 0.48(5k) + 0.40(6k) = 480, so 2.4k + 2.4k = 480, giving 4.8k = 480 and k = 100. Therefore y = 6k = Rs.600. Option C is correct.

Multiple choice

A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more for first 5 years, how much he will get now at the end of 7 years ?

  1. 1850

  2. 1838

  3. 1825

  4. Can't be determined

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

To calculate simple interest at different rates, we need the principal amount. The problem only states that Rs. 1750 is earned after 7 years at some rate, but doesn't specify the principal or the original rate. Without knowing whether 2% more means (r+2)% or 1.02r, and without the principal value, the interest cannot be determined.