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

A sum of money at simple interest amounts to Rs. 403 in 3 years at the rate of 10% per annum. What is the value of the sum?

  1. Rs. 400

  2. Rs. 380

  3. Rs. 310

  4. Rs. 345
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the simple interest formula A = P(1 + rt), where A = 403, r = 10% = 0.10, and t = 3 years. Substituting: 403 = P(1 + 0.10 × 3) = P(1.3). Therefore, P = 403/1.3 = 310. Option A (Rs. 400) and B (Rs. 380) are incorrect as they don't satisfy the formula.

Multiple choice

In how much time will a sum of Rs. 5250 amounts to Rs. 9870 at the rate of 11 percent per annum at simple interest ?

  1. 8 years

  2. 14 years

  3. 12 years

  4. 15 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple Interest = Principal × Rate × Time. Here: SI = 9870-5250 = Rs.4620, P = Rs.5250, R = 11%. Using the formula: 4620 = 5250 × 0.11 × T. Therefore, T = 4620/(5250 × 0.11) = 4620/577.5 = 8 years. After 8 years at 11% simple interest, Rs.5250 will amount to Rs.9870.

Multiple choice

A sum of money amounts to Rs. 767 in 3 years, and to Rs. 806 in 4 years on simple interest at 6% annum. What is the sum ?

  1. Rs. 600

  2. Rs. 560

  3. Rs. 675

  4. Rs. 650
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The difference between amounts after 4 years and 3 years (806 - 767 = 39) is the simple interest for one year. At 6% per annum, Principal = (Interest × 100) / (Rate × Time) = (39 × 100) / (6 × 1) = 650. Verification: Interest for 3 years = 650 × 6 × 3 / 100 = 117, so Amount = 650 + 117 = 767 ✓

Multiple choice

A car with a price of Rs. 6,50,000 is bought by making some down payment. On the balance, a simple interest of 10% is charged in lump sum and the money is to be paid in 20 equal annual instalments of Rs. 25,000. How much is the down payment ?

  1. Rs. 1,55,945

  2. Rs. 1,95,455

  3. Rs. 1,94,555

  4. Rs. 1,45,955
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P be the balance amount after down payment. Simple interest at 10% on P is 0.1P, so total payable = P + 0.1P = 1.1P. This equals 20 × 25,000 = 5,00,000. Therefore 1.1P = 5,00,000, giving P = 4,54,545 (approx). Down payment = 6,50,000 - 4,54,545 = 1,95,455. Option B matches.

Multiple choice

Find the compound interest on ₹35,000 in 2 years at 6% per annum, the interest being compounded half-yearly (nearest to a ₹):

  1. ₹4,000

  2. ₹4,193

  3. ₹4,393

  4. ₹4,388
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Principal = 35,000, rate = 6% p.a. compounded half-yearly means 3% per half-year for 4 periods. Amount = 35000(1.03)⁴ = 35000 × 1.1255 = 39,393. Compound Interest = 39,393 - 35,000 = 4,393. Option C matches this calculation. Verify: (1.03)⁴ = 1.1255088, times 35000 = 39392.8, nearest rupee is 39393.

Multiple choice

A sum of ₹5,000 was deposited for 3 years at 10% per annum, compounded annually. The difference between the interest for 2 years and that for 3 years is:
  1. $₹ 560$
  2. $₹ 506$
  3. $₹ 650$
  4. $₹ 605$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

CI for 2 years: 5000(1.1² - 1) = 5000 × 0.21 = 1050. CI for 3 years: 5000(1.1³ - 1) = 5000 × 0.331 = 1655. Difference: 1655 - 1050 = 605. Alternatively, the extra interest in year 3 is 10% of the amount after year 2: (5000 × 1.21) × 0.10 = 6050 × 0.10 = 605.

Multiple choice

A sum of Rs. 3000 becomes Rs. 6000 when invested in a scheme of simple interest. If the amual rate of interest and the number of years for which the sum was invested are same, then what is the annual rate of interest?

  1. 5 percent

  2. 20 percent

  3. 10 percent

  4. 15 percent
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For simple interest: Amount = Principal + (P×R×T)/100. Given P=3000, Amount=6000, so Interest=3000. Since R=T (rate equals time), we have 3000 = (3000×R×R)/100, which gives R²=100, so R=10%. Checking: 3000 + (3000×10×10)/100 = 3000 + 3000 = 6000.

Multiple choice

The difference between simple interest and compound interest on a certain sum of money for 2 years at 8 % per annum is ₹ 256. Find the sum. एक निश्चित राशि पर 2 वर्ष के लिए 8% प्रति वर्ष की दर से साधारण ब्याज और चक्रवृद्धि ब्याज का अंतर ₹ 256 है। राशि ज्ञात कीजिए।

  1. ₹ 20000

  2. ₹ 30000

  3. ₹ 35000

  4. ₹ 40000

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

Difference between CI and SI for 2 years = P × r²/10000. Given: 256 = P × 8²/10000 = P × 64/10000. So P = 256 × 10000/64 = 256 × 156.25 = ₹40,000. The formula for 2-year difference at rate r% is P(r/100)².

Multiple choice

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? What is the difference between the simple interest and compound interest on a certain amount? I. Rate of interest is 5% per annum. II. The interest at the end of 5 years is Rs. 1250.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the difference between simple interest (SI) and compound interest (CI), we need the principal amount (P), rate (R), and time (T). Statement I gives rate = 5%. Statement II gives interest = Rs. 1250 after 5 years, but doesn't specify whether this is SI or CI, and doesn't give the principal. Even together, we cannot determine the principal uniquely because we don't know which type of interest the Rs. 1250 represents. Both statements together are insufficient.

Multiple choice

A person invested some amount at the rate of 12% simple interest and the remaining at 10%. He received yearly an interest of Rs. 130. Had he interchanged the amounts invested, he would have received an yearly interest of Rs. 134. How much money did he invest at different rates? एक व्यक्ति ने कुछ राशि 12% की दर से साधारण ब्याज पर और शेष राशि 10% पर निवेश किया । उसे सालाना 130 रूपये का ब्याज मिला। यदि उसने निवेश की गई राशियों को अदला - बदली कर दी होती तो उसे 134 रूपये का सालाना ब्याज प्राप्त होता। उसने भिन्न दरों पर कितनी राशि निवेश की?

  1. Rs.500 @ 10%, Rs.800 @ 12%

  2. Rs.700 @ 10%, Rs.600 @ 12%

  3. Rs.800 @ 10%, Rs.400 @ 12%

  4. Rs.700 @ 10%, Rs.500 @ 12%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let amount at 12% = x and at 10% = y. Then 0.12x + 0.10y = 130 and 0.10x + 0.12y = 134. Subtracting: -0.02x + 0.02y = 4, so y - x = 200. From first eq: 12x + 10(x + 200) = 13000 gives 22x + 2000 = 13000, so 22x = 11000, x = 500, y = 700. So Rs. 500 at 12%, Rs. 700 at 10%. Option D has this.

Multiple choice

Pari invests Rs.35500 in a scheme which earns her simple interest at the rate of 15 p.c.p.a. two years she reinvests the principal amount plus interest earned in another scheme which earns her compound interest at the rate of 20 p.c.p.a. What will be the total interest earned by Pari over the principal amount at the end of 5 years? परी एक योजना में रु.35500 का निवेश करती है जिससे उसे 15 प्रतिशत वार्षिक ब्याज की दर से साधारण ब्याज प्राप्त होता है वह पुनः मूलधन राशि और ब्याज को दूसरी योजना में निवेश करती है जिससे उसे 20 प्रतिशत वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज की दर से प्राप्त होता है। परी के द्वारा किया गया 5 वर्षों में मूलधन राशि पर प्राप्त कुल ब्याज क्या है?

  1. Rs./रु.30956.80

  2. Rs./रु.35017.20

  3. Rs./रु.43597.80

  4. Rs./रु.44247.20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Year 1-2: Simple Interest = 35500 × 15% × 2 = Rs.10650. Amount after 2 years = 35500 + 10650 = Rs.46150. Year 3-5 (3 years of Compound Interest at 20%): 46150 × (1.20)^3 - 46150 = 46150 × 1.728 - 46150 = 79747.20 - 46150 = Rs.33597.20. Total interest = 10650 + 33597.20 = Rs.44247.20. The problem involves two phases: simple interest for 2 years, then compound interest for 3 years on the accumulated amount.

Multiple choice

Alok invested some amount at the rate of 12% simple interest and some another amount at the rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested he would have received Rs. 4 more as interest. How much amount did he invest at 12% simple interest ? आलोक कुछ धनराशि 12% साधारण ब्याज पर कुछ दूसरी धनराशि 10% साधारण ब्याज पर निवेश करता है। वह वार्षिक ब्याज रू. 130 प्राप्त करता है। लेकिन यदि निवेशित की राशियों को आपस में बदल दे तो वह 4 रू. अधिक ब्याज के रूप में प्राप्त करता है। उसने 12% साधारण ब्याज पर कितना धन निवेश किया ?

  1. Rs. 700

  2. Rs. 500

  3. Rs. 800

  4. Rs. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let amount at 12% be x, at 10% be y. Then 0.12x+0.10y=130. If interchanged: 0.12y+0.10x=134. Subtracting: 0.02y-0.02x=4 → 0.02(y-x)=4 → y-x=200. Solving: from first eq, 12x+10y=13000. Using y=x+200: 12x+10(x+200)=13000 → 22x=11000 → x=500. Amount at 12%=Rs.500.