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

If the simple interest for 5 years is Rs. 77.50, find the simple interest for 4 years for the same principal and rate

  1. Rs. 124

  2. Rs. 15.5

  3. Rs. 387.5

  4. Rs. 62
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest is directly proportional to time. If SI for 5 years is Rs. 77.50, then SI for 1 year = 77.50/5 = Rs. 15.50. Therefore, SI for 4 years = 4 × 15.50 = Rs. 62. Option A (Rs. 124) would be for 8 years, option B (Rs. 15.5) is for 1 year, and option C (Rs. 387.5) is incorrectly calculated.

Multiple choice

Naveen divides Rs 30563 among Sona, Mona, and Kavita, so that if the amounts being invested at 4% simple interest, the amounts received after 2, 3 and 4 years by Sona, Mona, and Kavita respectively is equal. Find the share of Mona?

  1. Rs. 10179

  2. Rs. 11379

  3. Rs. 11579

  4. Rs. 11879

  5. Rs. 12179
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let shares be x, y, z for 2, 3, 4 years at 4% SI. Equal amounts means x(1 + 0.08) = y(1 + 0.12) = z(1 + 0.16). So 1.08x = 1.12y = 1.16z. Ratio x:y:z = 1/1.08 : 1/1.12 : 1/1.16 = 100/108 : 100/112 : 100/116 = 25/27 : 25/28 : 25/29. Total = 25/27 + 25/28 + 25/29 = 25(1/27 + 1/28 + 1/29). Mona's share = (25/28) / [25(1/27 + 1/28 + 1/29)] × 30563. After calculation: share is proportional to 1/(1 + 0.04t). Ratio x:y:z = 1/1.08 : 1/1.12 : 1/1.16. Multiplying by LCM: 26.57 : 25.59 : 24.78. Total parts ≈ 76.94. Mona's share = 25.59/76.94 × 30563 ≈ 10179.

Multiple choice

The difference in simple and compound interest on a certain sum for 2 years at 5% per annum is Rs 75. Find the sum?

  1. Rs.40000

  2. Rs.20000

  3. Rs.50000

  4. Rs.30000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Rs 75 difference comes from compound interest calculating interest on the first year's interest. For 2 years at 5%, this difference equals P × (5/100)² = P × 0.0025. Setting this equal to 75 gives P = 75/0.0025 = Rs 30000. Simple interest stays the same each year, while compound interest includes interest on interest.

Multiple choice

What is the rate of interest? (1) If the principle becomes eight times of itself in five years. (2) If the ratio between the interest and the principle is 3 : 10

  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 statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: Principal becomes 8 times in 5 years. For simple interest: P + SI = 8P, so SI = 7P over 5 years, Rate = (7P/5P) × 100 = 140% per 5 years or 28% per annum. For compound interest: P(1 + r/100)⁵ = 8P, so (1 + r/100)⁵ = 8, giving r ≈ 51.6%. Either way, statement I alone is sufficient. Statement II: Interest/Principal = 3/10 gives SI = 0.3P, but without time period we cannot find rate. Insufficient. Option A is correct.

Multiple choice

Ganesh borrowed a sum at SI. What is the amount returned in 2 years? I. The rate of interest is 4% PA. II. The SI incurred on the sum in 1 year is Rs. 500. III. The borrowed sum is 10 times the amount earned as SI in 2 years.

  1. Only I and II

  2. Only I and III

  3. I, II and III together not sufficient

  4. II and either I or III

  5. All I, II and III
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From I and II: SI in 1 year is Rs. 500 at 4% rate, so principal P = 500/0.04 = Rs. 12,500. SI in 2 years = 500 × 2 = Rs. 1000. Amount returned = P + SI = 12,500 + 1000 = Rs. 13,500. This is sufficient. From II alone: SI = Rs. 500/year, but we need rate or principal to find total amount, so insufficient. From III alone: Borrowed sum = 10 × SI in 2 years, but we don't know the actual SI value, so insufficient. II with either I or III works.

Multiple choice

The difference between the compound interest and simple interest of a certain sum of amount is rupees 256.40 for 4 years at 10% rate per annum. Find the sum of money?

  1. 4000

  2. 4500

  3. 40000

  4. 6000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the difference between compound interest and simple interest for n years is CI - SI = P[(1 + r)^n - 1 - nr]. For 4 years at 10%: (1.1)^4 = 1.4641, so CI - SI = P[1.4641 - 1 - 0.4] = P(0.0641). Given CI - SI = 256.40, we have P = 256.40 / 0.0641 = 4000. Option A (4000) is correct. Option B (4500) is close but incorrect. Option C (40000) is ten times the correct value.

Multiple choice

The simple interest occured on a sum of certain principal is Rs. 35,6727 in seven year at the rate of 8 p.c.p.a. What would be the compound interest occured on that principal at the rate of 2 p.c.p.a in 2 years ?

  1. Rs. 2573.48

  2. Rs. 18435

  3. Rs. 19345

  4. Rs. 19435

  5. Rs. 20134
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

SI = P×R×T/100, so 35672.7 = P×8×7/100 = 56P/100. P = 3567270/56 = Rs. 63,443.75. CI at 2% for 2 years = P(1 + 2/100)² - P = 63443.75×1.0404 - 63443.75 = 63443.75×0.0404 = Rs. 2,563.13. The answer shows Rs. 2573.48. Let me recalculate: (1.02)² = 1.0404. CI = 63443.75 × 0.0404 = 2563.12. There's a slight discrepancy with the given answer, possibly due to rounding in the principal amount. If we use P = 63708.33 (from 35672.7×100/56), CI = 63708.33×0.0404 = 2573.81. The answer option A (2573.48) is approximately correct given rounding. Options B, C, D, and E are significantly incorrect.

Multiple choice

A man deposited Rs.20000 in a bank for two years at 20% per annum. If the interest is compounded half-yearly during the first year and compounded annually during the second year then what is the total interest he will receive after two years.

  1. 8200

  2. 8800

  3. 9040

  4. 9000

  5. 9400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the first year with half-yearly compounding at 20% per annum, the rate per half-year is 10%. Amount after first year = 20000 × (1.10)² = 20000 × 1.21 = Rs. 24200. For the second year with annual compounding at 20%, amount after second year = 24200 × 1.20 = Rs. 29040. Total interest = 29040 - 20000 = Rs. 9040.

Multiple choice

A sum of money becomes Rs 35280 after 2 years and Rs 37,044 after 3 years when lent on compound interest. Find the principal amount.

  1. Rs. 32000

  2. Rs. 34200

  3. Rs. 36400

  4. Rs. 38800

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

Amount after 2 years = Rs 35280. Amount after 3 years = Rs 37044. The difference Rs 37044 - Rs 35280 = Rs 1764 is the compound interest for the 3rd year on Rs 35280. So interest rate r = (1764/35280) × 100 = 5%. If amount after 2 years is Rs 35280 at 5% CI, then P(1.05)² = 35280, so P = 35280/(1.1025) = 35280 × 10000/11025 = Rs 32000. Verification: 32000 × 1.05² = 32000 × 1.1025 = Rs 35280 ✓ and 35280 × 1.05 = Rs 37044 ✓

Multiple choice

The compound interest on a certain amount for 2 years at the rate of 8% per annum is Rs.312 .What will be the simple interest on the same amount at same rate and same time?

  1. Rs.349.92

  2. Rs. 300

  3. Rs. 296.92

  4. Rs. 200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P be the principal amount. Compound interest for 2 years at 8% is P[(1.08)^2 - 1] = P[1.1664 - 1] = 0.1664P = 312. Solving gives P = 1875. Simple interest = Prt = 1875 × 0.08 × 2 = 300. Option A (Rs. 349.92) incorrectly uses the compound interest formula again. Option C is a calculation error.

Multiple choice

What is the difference between the compound interest and simple interest accrued on an amount of Rs. 16200 at the end of 3 year at the rate of 25%?

  1. Rs. 3234.36

  2. Rs. 3420.64

  3. Rs. 3290.63

  4. Rs. 4208.08
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest for 3 years at 25% on Rs. 16200: SI = (16200 × 25 × 3)/100 = Rs. 12150. Compound Interest: Year 1: 16200 × 1.25 = 20250; Year 2: 20250 × 1.25 = 25312.5; Year 3: 25312.5 × 1.25 = 31640.63. CI = 31640.63 - 16200 = Rs. 15440.63. Wait - this doesn't match the options. Let me recalculate more carefully: P = 16200, r = 25%, n = 3 years. SI = 16200 × 0.25 × 3 = 12150. CI = 16200 × (1.25)^3 - 16200 = 16200 × 1.953125 - 16200 = 31640.63 - 16200 = 15440.63. CI - SI = 15440.63 - 12150 = 3290.63, which matches option C exactly.