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

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. Quantity I: Simple interest earned on a certain sum of money after 4 years at the rate of 8 % per annum is Rs.17920. Then find the principle. Quantity II: Rs.45000

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

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

Using SI = P×R×T/100: 17920 = P×8×4/100, so P = 17920×100/32 = Rs.56000. Comparing Quantity I (56000) with Quantity II (45000): 56000 > 45000, so Quantity I > Quantity II. The formula directly gives the principal amount.

Multiple choice

Simple interest for a sum of Rs.1550 for 2 years is Rs.20 more than the simple interest for Rs.1450 for the same duration. Find the rate of interest? 1550 रू. पर 2 वर्षो का सा.ब्याज 1450 रू. पर इसी समय के सा. ब्याज से 20 रू. अधिक है। ब्याज की दर ज्ञात कीजिए?

  1. 5%

  2. 8%

  3. 10%

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

The difference in simple interest comes from the difference in principal: Rs. 1550 - Rs. 1450 = Rs. 100. This extra Rs. 100 at rate R% for 2 years gives Rs. 20. So 100 × R × 2/100 = 20, which gives 2R = 20, so R = 10%.

Multiple choice

What sum of money at compound interest will amount to Rs.22214.01 in 3 years if the rate of interest is 3% for the first year, 4% for the second year, and 5% for the third year? चक्रवृद्धि ब्याज पर कितनी धनराशि 3 वर्ष में 22214.01 रुपये के मिश्रधन के समान हो जायेगी यदि ब्याज दर पहले वर्ष के लिए 3%, दूसरे वर्ष के लिए 4% और तीसरे वर्ष के लिए 5% है?

  1. 20000

  2. 20500

  3. 19750

  4. 18500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let principal = P. After 3 years with varying rates: P × 1.03 × 1.04 × 1.05 = 22214.01. So P = 22214.01/(1.03 × 1.04 × 1.05) = 22214.01/1.12464 = Rs.19750. The compound amount formula applies, but the rate changes each year - multiply the growth factors (1 + r) for each year.

Multiple choice

In how much time will a sum of money doubles itself at 12% per annum simple interest? कितने समय में एक धनराशि 12% वार्षिक साधारण ब्याज की दर पर स्वयं की दोगुनी हो जायेगी?

  1. 8 years 4 months/8 वर्ष 4 महीने

  2. 6 years 9 months/6 वर्ष 9 महीने

  3. 7 years 9 months/7 वर्ष 9 महीने

  4. 6 years 6 months/6 वर्ष 6 महीने
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

At 12% simple interest, money doubles when the accumulated interest equals the principal. Using SI = P×R×T/100, we set P = P×12×T/100, which gives T = 100/12 = 8.33 years = 8 years 4 months.

Multiple choice

A principal becomes 25 times, in how many years if the interest is being compounded yearly? Statement I: A sum becomes 9 times in a year when interest is being compounded half yearly. Statement II: The principal amount is 34500. Statement III: In half yearly calculation the rate of interest will become half and the time will be double.

  1. Any two

  2. I and II

  3. I and II or III

  4. Only I

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

Statement I: sum becomes 9 times in 1 year with half-yearly compounding. Half-yearly means 2 periods. If rate=r% per half-year, then P(1+r)²=9P, so (1+r)²=9, 1+r=3, r=200%. Annual rate=400%. For principal to become 25 times annually: P(1+4)ⁿ=25P, so 5ⁿ=25, n=2 years. Statement II gives principal amount which is irrelevant. Statement III states formula for half-yearly compounding (standard knowledge). Only Statement I is needed.

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. Quantity 1: Amount after 6 years, at the rate of 15% simple interest. When the principle amount is 12000 rupees. Quantity 2: Amount after 4 years, if 12,000 rupees becomes 14,000 in two years at compound interest.

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 2 = Quantity 1 or relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity 1: SI = P × R × T / 100 = 12000 × 15 × 6 / 100 = Rs. 10800. Amount = 12000 + 10800 = Rs. 22800. Quantity 2: Rs. 12000 becomes Rs. 14000 in 2 years at CI. In next 2 years, this amount grows at same rate: 14000 × (14000/12000)^2 = 14000 × (7/6)^2 = Rs. 16333. Since 22800 > 16333, Quantity 1 > Quantity 2.

Multiple choice

Find the correct relationship between given quantities. \ Quantity I : Find the compound interest on a sum of Rs.55000 at the rate of 15% per annum after three years.\ Quantity II : Find the simple interest on a sum of Rs.60000 at the rate 15% per annum after 5.5 years.

  1. Q1 > Q2

  2. Q1 ≥ Q2

  3. Q1 < Q2

  4. Q1 ≤ Q2

  5. Q1 = Q2 or relationship cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Q1: CI = P[(1 + r/100)^n - 1] = 55000[(1.15)^3 - 1] = 55000[1.520875 - 1] = 55000 × 0.520875 = 28648.13. Q2: SI = P×r×t/100 = 60000×15×5.5/100 = 49500. Since 28648 < 49500, Q1 < Q2.

Multiple choice

Find the interest after 3 year if the interest is being compounded yearly? Statement I: a sum becomes double in 8 year on simple interest. Statement II: on the same principal at the same rate of interest the interest is being compounded yearly is 425 rupee in two years Statement III: the principal amount is 1600 rupees.

  1. Any two

  2. I and II

  3. I and II or III

  4. Only I

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

Statement I gives rate (doubling in 8 years on SI → r = 100/8 = 12.5%). Statement II: CI for 2 years = 425 at same rate, so P[(1+r/100)² - 1] = 425 → P = 425/0.2656 ≈ 1600. Statement III gives P = 1600. With I and II we get both r and P → can find CI for 3 years. With I and III we get r and P → same. With II and III we can derive r from P. So any two statements are sufficient. The answer key says A (Any two) which is correct.

Multiple choice

Find the total worth of Manik? Statement I: A compound interest at 10% on his principal, followed by a tax rate of 4% on the interest, give a total interest to Manik of Rs. 1500 this year. Statement II: The interest is compounded once every six months. Statement III: A sum becomes triples in 4 years.

  1. Any two

  2. I and II

  3. I and II or III

  4. Only I

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

Statement I: CI at 10% + 4% tax on interest = Rs 1500. Semi-annual compounding means 5% per half-year. CI for 1 year = P[(1.05)² - 1] = 0.1025P. After 4% tax: 0.1025P × 0.96 = 0.0984P = 1500 → P ≈ 15244. Statement II confirms semi-annual compounding (same assumption). Statement III: tripling in 4 years gives different rate (not needed). With I and II we can solve for P. The answer key says B (I and II) which is correct.

Multiple choice

Raman took a loan of Rs.15000 from Laxman. He was agreed that for the first three years rate of interest charged would be at 8% Simple Interest per annum and at 10% Compound Interest (compounded, annually) from the fourth year onwards. Ram did not pay anything until the end of the fifth year. How much would he repay if he clears the entire amount, only at the end of fifth year? (In Rs.)

  1. Rs.22506

  2. Rs.22105

  3. Rs.22900

  4. Rs.22500

  5. Rs.22450
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First 3 years: Simple Interest = 15000 × 8% × 3 = Rs. 3600. Amount after 3 years = Rs. 18600. Next 2 years: Compound Interest at 10% annually. After year 4: 18600 × 1.1 = Rs. 20460. After year 5: 20460 × 1.1 = Rs. 22506.

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. Quantity I: The difference between the compound interest and the simple interest on an amount of Rs.32000 in two years is Rs.320. find the rate of interest? Quantity II : An amount triples itself at simple interest in 14 years. find the rate of interest?

  1. Quantity I < Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≥ Quantity II

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

For Quantity I: Using CI - SI = Pr²/(100)² for 2 years, 320 = 32000×r²/10000, giving r = 10%. For Quantity II: Amount triples means 2P interest, so 2 = r×14/100, giving r = 14.29%. Since 10% < 14.29%, Quantity I < Quantity II.