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

sham borrowed a sum of Rs.4500 from bank at compound interest at 20% per annum. He pays back Rs.1500 at the end of each year. Calculate how much amount he will pay at the end of third year to clear all his dues?

  1. Rs.1020

  2. Rs.3816

  3. Rs.3814

  4. Rs.2500

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

Year 1: 4500 * 1.2 = 5400, after payment = 3900. Year 2: 3900 * 1.2 = 4680, after payment = 3180. Year 3: 3180 * 1.2 = 3816. Payment at end of year 3 = 3816 to clear dues.

Multiple choice

What will come at place of blank? Rs_ is invested at 12.5% compound interest. After 3 years the sum becomes Rs. 5467.5.

  1. 3840 Rs.

  2. 3520 Rs.

  3. 4080 Rs.

  4. 4250 Rs.

  5. 3675 Rs.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a compound interest problem where we solve for the principal (P). Using A = P(1 + r)^t, where A = 5467.5, r = 12.5% = 0.125, t = 3 years. Then P = A / (1.125)^3 = 5467.5 / 1.4238 ≈ 3840. The calculation (1.125)^3 = 1.423828125, and 5467.5 / 1.423828125 = 3840 exactly. Option A (Rs. 3840) is correct.

Multiple choice

A sum of money become 17280 rupees after 2 years and become 24883.2 rupees after 4 year if the rate of interest is compounded annually. Find the rate of interest.

  1. 15%

  2. 20%

  3. 25%

  4. 22.5%

  5. 27.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For compound interest, if amount after 2 years is 17280 and after 4 years is 24883.2, the ratio of amounts after successive 2-year periods should be constant. Testing 20%: 17280 × 1.2 = 20736.04; then 20736.04 × 1.2 = 24883.2. This confirms 20% is correct. Working backwards: If principal is P, then P × (1.2)² = 17280, so P = 12000.

Multiple choice

Rs. 2000 amounts to Rs. 2600 in five years at a certain rate of simple interest. If interest is 3 % more than the previous rate, then in the same time period, the same sum will amount to

  1. Rs.2700

  2. Rs.2800

  3. Rs.2900

  4. Rs.3000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interest earned = Rs. 2600 - Rs. 2000 = Rs. 600 over 5 years. Original rate = (600 × 100)/(2000 × 5) = 6%. New rate = 6% + 3% = 9%. New interest = (2000 × 9 × 5)/100 = Rs. 900. New amount = Rs. 2000 + Rs. 900 = Rs. 2900.

Multiple choice

A man invested two equal sums of money, one at 10% per annum, interest compounded half-yearly and the second part at a certain percent, interest compounded annually. If he gets equal amounts after 3 years, what is the rate of interest on second investment?

  1. 9.75%

  2. 10%

  3. 10.75%

  4. 10.25%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the first investment at 10% compounded half-yearly, the effective rate is (1 + 0.10/2)² - 1 = 0.1025 or 10.25% annually. After 3 years, the amount is P(1.1025)³. For the second investment at rate r compounded annually, the amount is P(1+r)³. Since amounts are equal: (1.1025)³ = (1+r)³, giving r = 0.1075 or 10.75%.

Multiple choice

Each question contains a statement followed by Quantity I and Quantity II. Read the contents clearly and answer your questions accordingly. Quantity I: The simple interest on a certain sum of money for 5 years at 8% per annum is Rs.7500. Then find the principal. Quantity II: The compound interest on a certain sum of money for 2 years at 20% per annum is Rs.8800. Then find the principal.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity II ≥ Quantity I

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

Quantity I: SI = P*R*T/100. 7500 = P*8*5/100, so P = 7500*100/40 = Rs.18,750. Quantity II: CI = P[(1+R/100)^n - 1]. 8800 = P[(1.2)^2 - 1] = P[1.44 - 1] = 0.44P. So P = 8800/0.44 = Rs.20,000. Since 20,000 > 18,750, Quantity II is greater. Option A is correct.

Multiple choice

Arvind deposited a sum of money with a bank on 1st January, 2014 at 8% simple interest per annum. He received an amount Rs. 3, 144 on 7th August, 2014./अरविन्द ने एक धनराशि 1 जनवरी 2014 को बैंक में 8% वार्षिक साधारण ब्याज की दर से निवेश की, उसे रू. 3,144 की धनराशि 7 अगस्त, 2014 को बैंक से प्राप्त हुई। उसने कितनी धनराशि बैंक में निवेश की थी?

  1. Rs.3,080

  2. Rs.3,000

  3. Rs.2,500

  4. Rs.3,100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time period: Jan 1 to Aug 7, 2014 = 31+28+31+30+31+30+31+7 = 219 days = 219/365 years. Simple Interest = P × R × T = Amount - Principal. 3144 - P = P × 8/100 × 219/365. 3144 - P = P × 0.08 × 0.6 = 0.048P. 3144 = 1.048P. P = 3144/1.048 ≈ Rs. 3,000.

Multiple choice

A sum amounts to Rs.11638 in 2 years and to Rs.13383.7 in 3 years compounded annually. Find the sum and the rate of interest per annum. एक धनराशि चक्रवृद्धि ब्याज की दर से 2 वर्षों में 11638 रु. और 3 वर्षों में 13383.7 रु. हो जाती है | धनराशि और प्रति वर्ष ब्याज की दर ज्ञात कीजिये |

  1. Rs. /रु.8250, 15%

  2. Rs. /रु.8550, 12%

  3. Rs. /रु.8880, 18%

  4. Rs. /रु.8800, 15%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be principal, r be rate. P(1 + r/100)² = 11638 and P(1 + r/100)³ = 13383.7. Dividing: 1 + r/100 = 13383.7/11638 = 1.15, so r = 15%. Substituting back: P = 11638/(1.15)² = 11638/1.3225 = 8800. Verify: 8800 × 1.3225 = 11638 ✓ and 8800 × 1.520875 = 13383.7 ✓.

Multiple choice

If a sum of money amounts to Rs 1540 in 12 years with a rate of 12% compound interest, then what will be the interest in 13th year for the same amount at the same rate of interest?

  1. Rs 184.8

  2. Rs 154.4

  3. Rs 144.8

  4. Rs 154.8

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

Amount after 12 years at 12% CI = Rs 1540. Principal P = 1540 / (1.12)^12 ≈ 1540 / 3.896 ≈ Rs 395.3. Interest in 13th year = Amount at end of 13th year - Amount at end of 12th year = P(1.12)^13 - P(1.12)^12 = P(1.12)^12(1.12 - 1) = 1540 × 0.12 = Rs 184.8. This is because CI interest for any year = 12% of previous year's amount.

Multiple choice

What is the rate of simple interest for the first 5 years if the sum of Rs 750 becomes Rs 1240 in 8 years and the rate of interest for the last 3 years is 4%?

  1. 32/3%

  2. 30%

  3. 28%

  4. 18%

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

Total interest earned = Rs 1240 - Rs 750 = Rs 490 over 8 years. For last 3 years at 4%, interest = 750 × 4/100 × 3 = Rs 90. This leaves Rs 490 - Rs 90 = Rs 400 as interest for first 5 years. Let rate for first 5 years be r%. Then 750 × r/100 × 5 = 400, so r = (400 × 100)/(750 × 5) = 40000/3750 = 10.67% = 32/3%.

Multiple choice

A took a certain sum of money from B as a loan at the rate of 7\% simple interest per annum. A lends the same amount to C at simple interest of 12\% per annum. If at the end of 7 years A makes a profit of Rs 1050, then what amount did C borrow from A?

  1. Rs 3200

  2. Rs 3000

  3. Rs 3500

  4. Rs 3050

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

A borrows money at 7% simple interest and lends it at 12% simple interest, earning the difference of 5% per year. Over 7 years, this difference amounts to 35% of the principal (5% × 7 = 35%), which equals Rs 1050. Solving 0.35P = 1050 gives the principal as Rs 3000, which is the amount C borrowed from A.

Multiple choice

Following question consists a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question or not. What is the total compound interest on a sum after two years? (I) The interest after one year is Rs.10 and the sum is Rs. 100. (II) The difference between simple and compound interest on a sum of Rs. 100 at the end of two years is Rs. 1.

  1. Only II

  2. Only I

  3. Both I and II

  4. Any one of the two.

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

From Statement I: Interest after 1 year is Rs.10 on principal Rs.100, so rate = 10%. Compound interest for 2 years at 10% = 100(1.1)² - 100 = Rs.21. From Statement II: For 2 years, difference between CI and SI = P(r/100)² = Rs.1. With P=100, we get 100(r/100)² = 1, giving r = 10%. CI for 2 years = Rs.21. Either statement alone is sufficient.

Multiple choice

Shivani invested Rs.18000 in two different parts and the interest received at the rate of 8% SI for two years is equal to the interest received at the rate of 10% interest for two years. Find the difference between the Sum invested in 10% and 8%.

  1. Rs.1000

  2. Rs.2000

  3. Rs.3000

  4. Rs.4000

  5. Rs.2500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let amounts at 8% and 10% be x and y respectively. Interest equality: x*8*2/100 = y*10*2/100. Simplifying: 16x = 20y, so x/y = 20/16 = 5/4. Also x + y = 18000. Using ratio, if 9 parts = 18000, then 1 part = 2000. Difference |y - x| = |4-5| parts = 2000. The question asks for difference between 10% and 8% investments, which is Rs 2000.