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

Ram and Veer invested Rs P and Rs (P + 2250) on CI at the rate of 10% p.a. and 20% p.a. respectively. If both exchanged their investment then the sum of compound interest received by both earlier and now after two years is Rs 7962.5. Find the amount invested by Veer?

  1. Rs 6850

  2. Rs 6650

  3. Rs 7250

  4. Rs 7450

  5. Rs 7650
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P = Ram's investment. Original CI: Ram = P(1.1² - 1) = 0.21P, Veer = (P+2250)(1.2² - 1) = 0.44(P+2250). After exchanging: Ram = 0.21(P+2250), Veer = 0.44P. Total: 0.21P + 0.44(P+2250) + 0.21(P+2250) + 0.44P = 1.3P + 1462.5 = 7962.5. Solving: 1.3P = 6500, P = 5000. Veer's investment = P + 2250 = 7250.

Multiple choice

The ratio of two amounts is 4 : 5. If they are lent out at compound interest for 2 years and 1 year respectively, then the equal amount is received. Find the rate of interest per annum.

  1. 20%

  2. 30%

  3. 25%

  4. 21%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let amounts be 4x and 5x. Using compound interest formula A = P(1 + r/100)^t: 4x(1 + r/100)² = 5x(1 + r/100). Cancel x and (1 + r/100): 4(1 + r/100) = 5, so 1 + r/100 = 5/4 = 1.25. Therefore r/100 = 0.25 and r = 25%. Verify: 4(1.25)² = 4(1.5625) = 6.25, and 5(1.25) = 6.25. Equal amounts received.

Multiple choice

RS 6000 becomes Rs 7200 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times itself, the amount of the same principle in 5 years will be

  1. Rs 8000

  2. Rs 8250

  3. Rs 9250

  4. Rs 9000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest = 7200 - 6000 = Rs 1200 over 4 years. Annual interest = 1200/4 = Rs 300. Rate = 300/6000 × 100 = 5% per annum. New rate = 1.5 × 5 = 7.5%. Interest in 5 years at 7.5% = 6000 × 7.5/100 × 5 = Rs 2250. Amount = 6000 + 2250 = Rs 8250.

Multiple choice

What is the compound interest on Rs. 20000 for 3 years if the rate of interest is 5% for the first year, 10% for the second year and 15% for the third year? रू. 20000 पर 3 वर्षों के लिए चक्रवृद्धि ब्याज क्या होगा यदि प्रथम वर्ष ब्याज की दर 5% दूसरे वर्ष ब्याज की दर 10% तथा तृतीय वर्ष 15% है?

  1. Rs. 6565

  2. Rs. 5656

  3. Rs. 6655

  4. Rs. 6554

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

Principal = Rs. 20000. Year 1 at 5%: 20000 × 1.05 = Rs. 21000. Year 2 at 10%: 21000 × 1.10 = Rs. 23100. Year 3 at 15%: 23100 × 1.15 = Rs. 26565. Compound Interest = Final Amount - Principal = 26565 - 20000 = Rs. 6565. Therefore, the compound interest is Rs. 6565.

Multiple choice

Mr. Surendra invested Rs.20000 with rate of interest at 20 p.c.p.a. The interest was compounded half yearly for the first year and in the next year it was compounded yearly. What will be the total interest earned at the end of two years? श्री सुरेन्द्र ने 20 वार्षिक ब्याज दर पर Rs. 20000 का निवेश किया। पहले साल में ब्याज चक्रवृद्धि रूप से अर्द्धवार्षिक था और अगले साल इसे चक्रवृद्धि रूप से वार्षिक कर दिया गया था। दो साल के अंत में अर्जित कुल ब्याज क्या होगा?

  1. Rs.8800

  2. Rs.9040

  3. Rs.8040

  4. Rs.9800

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

Year 1 (half-yearly): P=20000, r=10% per half-year. After 1st half: 20000×1.1=22000. After 2nd half: 22000×1.1=24200. Year 2 (yearly): 24200×1.2=29040. Total interest = 29040-20000 = Rs. 9040. Option B is correct.

Multiple choice

The simple interest on a certain sum of money for 4 years at 12 percent per annum exceeds the compound interest on the same sum for 3 years at 10 percent per annum by Rs.1192. Find the sum. किसी निश्चित धनराशि पर 12 प्रतिशत वार्षिक ब्याज की दर से 4 वर्षों में साधारण ब्याज उसी धनराशि पर 3 वर्षों में 10% प्रतिशत वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज से 1192 रु. अधिक है | धनराशि ज्ञात कीजिये |

  1. Rs.9000

  2. Rs.8500

  3. Rs.8000

  4. Rs.10000

  5. Rs.7500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sum = P. Simple Interest for 4 years at 12% = P × 12 × 4 / 100 = 0.48P. Compound Interest for 3 years at 10% = P[(1.10)³ - 1] = P[1.331 - 1] = 0.331P. Given: 0.48P - 0.331P = 1192. So 0.149P = 1192. P = 1192 / 0.149 = 8000. The sum is Rs. 8000, which matches option C.

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. किसी मूलधन पर 2 वर्षो का साधारण ब्याज 108.80 रुपये है तथा समान मूलधन पर समान ब्याज दर पर समान समय का चक्रवृधि ब्याज 115.60 रुपये है। प्रति वर्ष ब्याज की दर ज्ञात कीजिये।

  1. 12.5 %

  2. 8%

  3. 10 %

  4. 15%

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

For 2 years, CI - SI = P(R/100)². Here 115.60 - 108.80 = 6.80 = P(R²/10000). Also SI = PR(2)/100 = 108.80. Solving: PR = 5440, so 6.80 = 5440R/10000, giving R = 12.5%. The difference between CI and SI for 2 years reveals the square of the rate.

Multiple choice

Rs. 600 becomes Rs. 708 in 3 years at certain simple rate of interest. If the rate of interest is increased by 5% what amount will Rs. 600 become in 3 years? रू.600 की राशि एक निश्चित ब्याज दर पर 3 वर्षों बाद रू. 708 हो जाती है। यदि ब्याज की दर 5% बढ़ा दी जाये तो रू. 600 की राशि तीन वर्षों बाद क्या होगी ?

  1. Rs. 758 रू. 758

  2. Rs. 798 रू. 798

  3. Rs. 804 रू. 804

  4. Rs. 850 रू. 850

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

Interest earned = 708 - 600 = 108 over 3 years. Annual interest = 108 ÷ 3 = 36. Rate = 36/600 = 6% per year. New rate = 6% + 5% = 11%. New interest = 600 × 0.11 × 3 = 198. New amount = 600 + 198 = 798. Option A uses 10% instead of 11%.

Multiple choice

An amount at 5 % compound interest for the first 2 years, followed by simple interest of 10% for the subsequent 3 years becomes Rs.25798.5. Find the initial amount. एक धनराशि पहले दो वर्षों में 5 % चक्रवृद्धि ब्याज की दर से, इसके बाद के तीन वर्षों के लिए 10% साधारण ब्याज की दर से 25798.5 रु. हो जाती है | मूल धनराशि ज्ञात कीजिये |

  1. 12000

  2. 14000

  3. 16000

  4. 18000

  5. 20000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be the principal. After 2 years at 5% compound interest: P(1.05)^2 = P(1.1025). After 3 more years at 10% simple interest on this amount: P(1.1025) × 1.3 = P(1.43325). Given final amount is 25798.5, so P = 25798.5 / 1.43325 = 18000. Verification: 18000(1.1025) = 19845, then 19845 × 1.3 = 25798.5.

Multiple choice

What will be compound interest on an amount of Rs.8400 at the rate of 13.5 p.c.p.a after 2 years? रू.8400 की राशि पर 13.5 प्र.श.प्र.व. की दर से 2 वर्ष के अंत में उपचित चक्रवृद्धि ब्याज क्या होगा?

  1. Rs.2256.18 रू.2256.18

  2. Rs.2019.38 रू.2019.38

  3. Rs.2421.09 रू.2421.09

  4. Rs.2615.08 रू.2615.08

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

CI = P[(1 + r/100)² - 1] for 2 years. P = 8400, r = 13.5%. CI = 8400[(1.135)² - 1] = 8400[1.288225 - 1] = 8400 × 0.288225 = 2421.09.

Multiple choice

If the difference between the simple interest and the compound interest earned on a certain amount @ 12% at the end of 3 years is Rs. 336.96, then what is the amount? यदि 3 वर्ष के अंत में एक निश्चित राशि पर 12% की दर से अर्जित साधारण ब्याज और चक्रवृद्धि ब्याज के बीच का अंतर रु. 336.96, तो राशि क्या है?

  1. Rs. 8550

  2. Rs. 8000

  3. Rs. 7500

  4. Rs. 8750

  5. Rs. 7700
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The difference between compound interest and simple interest for 3 years at rate r is P[(1 + r/100)³ - 1 - 3r/100]. For P = 7500, r = 12%, CI - SI = 7500[(1.12)³ - 1 - 0.36] = 7500[1.404928 - 1.36] = 7500 × 0.044928 = 336.96, which matches the given difference.