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

On a certain principal if simple interest for two years is Rs.10000 and compound interest is Rs.10625. What is the rate of interest ? यदि किसी निश्चित मूलधन पर दो वर्षों का साधारण ब्याज 10000 रू. और चक्रवृद्धि ब्याज 10625 रू. है तो ब्याज की दर क्या है ?

  1. 20%

  2. 15%

  3. 10%

  4. 12.5%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The difference between compound interest and simple interest for 2 years is the interest on the first year's simple interest. Simple interest for 2 years = 10000, so for 1 year = 5000. Difference = CI - SI = 10625 - 10000 = 625, which is interest on 5000 for 1 year. Rate = (625/5000) × 100 = 12.5%.

Multiple choice

600 amount to Rs. 740 in 5 years at a certain rate of simple interest. If the rate of interest is increased by 3%, what will be the amount then?
  1. $800$
  2. $856$
  3. $930$
  4. $830$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original amount: Rs. 600 becomes Rs. 740 in 5 years, so interest = Rs. 140. Rate = (140 × 100) / (600 × 5) = 14000 / 3000 = 4.67% per annum. New rate = 4.67% + 3% = 7.67%. New interest = 600 × 7.67% × 5 = Rs. 230. New amount = 600 + 230 = Rs. 830. The calculation checks out.

Multiple choice

Anita borrowed a certain sum of money from Ankita at the rate of 5% per annum simple interest for the first four years and at the rate of 7.5% per annum for the next six years and at the rate of 9% per annum for the period beyond ten years. If she pays a total of ` 86900 as interest only at the end of 15 years, how much money did she borrow?

  1. 72000 Rs.

  2. 75500 Rs.

  3. 80000 Rs.

  4. 79000 Rs.

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

Let P be principal. Interest for first 4 years at 5% = P × 5 × 4/100 = 0.2P. Interest for next 6 years at 7.5% = P × 7.5 × 6/100 = 0.45P. Interest for remaining 5 years (years 11-15) at 9% = P × 9 × 5/100 = 0.45P. Total interest = 0.2P + 0.45P + 0.45P = 1.1P. Given 1.1P = 86900, so P = 86900/1.1 = Rs.79000.

Multiple choice

Find the amount at the end of 3 years and 6 months- Statement I: If a principal is invested at the same rate of simple interest for 3 years it becomes 3 times. Statement II: The principal produces a compound interest of 1700 if invested at the same rate of interest for 2 years. Statement III: Any principal invested at the same rate of compound interest becomes 126.5625% at the end of 2 years.

  1. I and either II or III

  2. Any two

  3. II and either I or III

  4. II and III

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

Statement I: Principal becomes 3P in 3 years at SI, so rate r = 2P/3P = 2/3 per year. Statement II: CI for 2 years is 1700, so P(1+r)² - P = 1700. Statement III: P becomes 126.5625% of P after 2 years, so (1+r)² = 1.265625, giving r = 12.5%. II or III with I gives both r and P. From I, r = 2/3. Using r in II or III gives P. Then calculate amount at 3.5 years.

Multiple choice

A man earn compound interest of Rs. 831.0784 in 3 years at a rate of 8% per annum. Find the simple interest earned by him on same sum and same rate of interest in 4 years.

  1. 968 Rs.

  2. 1024 Rs.

  3. 1052 Rs.

  4. 1148 Rs.

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

Let the principal be P. Compound interest for 3 years at 8%: CI = P(1 + 0.08)³ - P = P(1.259712 - 1) = 0.124864P = 831.0784. So P = 831.0784/0.124864 ≈ 6656.78. Simple interest for 4 years at 8%: SI = P × 8% × 4 = 6656.78 × 0.08 × 4 ≈ 2130.17. Wait, this doesn't match. Let me recalculate: CI = P((1.08)³ - 1) = P × 0.259712 = 831.0784, so P = 831.0784/0.259712 ≈ 3200. Then SI = 3200 × 0.08 × 4 = 1024, making option B correct.

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.

  1. 2.43%

  2. 3.5%

  3. 4.4%

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

The difference between amounts after 7 years and 4 years is Rs. 75 (1200-1125), which is interest for 3 years. Annual interest = Rs. 25. Interest for 4 years = Rs. 100, so principal = 1125-100 = Rs. 1025. Rate = (100×100)/(1025×4) = 10000/4100 ≈ 2.439%, closest to 2.43%.

Multiple choice

If the rate of interest is 5% for first year, 6% for second year and 8% for third year. Then what is the C.I. on Rs.20000 for 3 years? यदि पहले वर्ष के लिए ब्याज दर 5%, दूसरे वर्ष के लिए 6% और तीसरे वर्ष के लिए 8% है, तो 20000 रु. के लिए 3 वर्षों का चक्रवृद्धि ब्याज कितना है?

  1. 4090.8

  2. 4040.8

  3. 4060.8

  4. 4045.8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After year 1: 20000 × 1.05 = 21000. After year 2: 21000 × 1.06 = 22260. After year 3: 22260 × 1.08 = 24040.8. CI = 24040.8 - 20000 = 4040.8. The amounts for each year are 1000, 1260, and 1780.8.

Multiple choice

Akhilesh invested Rs.30000 in a bank for 2 years at 12% per annum. How much money he should invest at 15% per annum for 2 years to get same interest which he got on previous principal. अखिलेश ने एक बैंक में 12% वार्षिक ब्याज की दर से दो वर्षों के लिए 30000 रू. निवेश किए । 15% वार्षिक ब्याज की दर से दो वर्षों के लिए उसे कितनी राशि निवेश करनी चाहिए जिससे उसे उतनी ही राशि ब्याज में मिले जितनी पहले मिलती थी ।

  1. Rs. 8000

  2. Rs. 27000

  3. Rs. 24000

  4. Rs. 35000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First investment: Interest = P × R × T = 30000 × 0.12 × 2 = Rs. 7200. For second investment at 15% for 2 years to give same interest: P × 0.15 × 2 = 7200. Therefore P = 7200/0.30 = Rs. 24000. Option A (Rs. 8000) would give much less interest, Option B (Rs. 27000) gives more, and Option D (Rs. 35000) gives even more.

Multiple choice

The compound interest for third year is Rs. 1053 on certain sum of money at certain rate of interest. On same sum of money at same rate of interest the second year compound interest is Rs. 936. Find the sum of money? किसी निश्चित धन पर किसी निश्चित ब्याज की दर से तीसरे वर्ष के लिए चक्रवृद्धि ब्याज 1053 रुपए है । उसी ब्याज की दर पर उसी धन पर द्वितीय वर्ष चक्रवृद्धि ब्याज 936 रुपए है । मूलधन ज्ञात कीजिये?

  1. Rs. 8854

  2. Rs. 6566

  3. Rs. 6656

  4. Rs. 7556
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The difference between CI for 3rd year and 2nd year is the interest on 2nd year's CI for one year: 1053 - 936 = 117. So 936 × r/100 = 117, giving r = 12.5%. CI for 1st year = 936/1.125 = 832. Total CI for 2 years = 832 + 936 = 1768. Principal P satisfies: P(1.125)² - P = 1768, so P = 1768/0.265625 = Rs. 6656.

Multiple choice

A person takes a loan of Rs. 40000 partly from a bank at 10% p.a. and remaining from another bank at 12% p.a. He pays total interest of ` 4440 per annum. Amount of loan taken from the first bank (in Rs.) is-

  1. Rs. 22000

  2. Rs. 20000

  3. Rs. 18000

  4. Rs. 16000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Rs x be from first bank at 10% and Rs(40000-x) from second bank at 12%. Total interest: 0.10x + 0.12(40000-x) = 4440. Solving: 0.10x + 4800 - 0.12x = 4440, so -0.02x = -360, giving x = 18000. This is a mixture problem using weighted interest rates.