Simple & Compound Interest MCQs for UPSC Prelims

43 practice questions on Simple & Compound Interest from the Quantitative Aptitude section of the UPSC Prelims syllabus. 43 come with a written explanation and 2 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

7 Easy 19 Medium 17 Hard 2 from past papers

Sample questions

Q1
Previous year question medium

A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct?

  1. A R = S
  2. B R > S
  3. C R < S
  4. D R ≤ S
Show answer and explanation

Correct answer: C - R < S

Same principal P grows to the same amount Q in one year under both schemes, so P(1 + R/200)^2 = P(1 + S/100). Expanding: 1 + R/100 + R^2/40000 = 1 + S/100, hence S = R + R^2/400. Since R > 0, S exceeds R, i.e. R < S - option (c). Intuitively, half-yearly compounding earns interest on interest within the year, so a smaller nominal rate R suffices to match the annually compounded rate S. Option (a) ignores intra-year compounding, option (b) reverses the inequality, and option (d) wrongly allows equality, which would need R = 0.

Q2
Previous year question medium

A person bought a refrigerator worth Rs. 22,800 with 12.5% interest compounded yearly. At the end of first year he paid Rs. 8,650 and at the end of second year Rs. 9,125. How much will he have to pay at the end of third year to clear the debt?

  1. A Rs. 9,990
  2. B Rs. 10,000
  3. C Rs. 10,590
  4. D Rs. 11,250
Show answer and explanation

Correct answer: D - Rs. 11,250

Interest rate 12.5% = 1/8, so each year the balance is multiplied by 1.125. Year 1: 22,800 x 1.125 = 25,650; after paying 8,650, balance = 17,000. Year 2: 17,000 x 1.125 = 19,125; after paying 9,125, balance = 10,000. Year 3: 10,000 x 1.125 = 11,250, which must be paid in full to clear the debt. Answer is Rs. 11,250.

Q3
hard

On a principal of Rs. 8,000 at 10% per annum, what is the difference between the compound interest (compounded annually) and the simple interest over a period of 3 years?

  1. A Rs. 240
  2. B Rs. 248
  3. C Rs. 256
  4. D Rs. 264
Show answer and explanation

Correct answer: B - Rs. 248

Simple interest for 3 years = 8000 x 10 x 3 / 100 = Rs. 2,400. Compound amount = 8000 x (1.1)^3 = 8000 x 1.331 = Rs. 10,648, so CI = 2,648. Difference = 2,648 - 2,400 = Rs. 248. This matches the formula for the 3-year difference: P(r/100)^2 x (3 + r/100) = 8000 x 0.01 x 3.1 = 248.

Q4
medium

A sum of money becomes Rs. 2,420 in 2 years and Rs. 2,662 in 3 years under compound interest, compounded annually. What is the annual rate of interest?

  1. A 10%
  2. B 12%
  3. C 8%
  4. D 11%
Show answer and explanation

Correct answer: A - 10%

Under compound interest, the amount grows by the same factor each year. The interest earned in the third year = 2662 - 2420 = 242, and this is the interest on the amount at the end of year 2 (Rs. 2420). So the rate = 242 / 2420 = 0.10 = 10%. Verify: 2420 x 1.10 = 2662, correct. Option 12% gives 2420 x 1.12 = 2710.4, wrong. Option 8% gives 2613.6, wrong. Option 11% gives 2686.2, wrong. The rate is 10%.

Q5
hard

The difference between the compound interest and the simple interest on a certain sum for 2 years at 8% per annum is Rs. 32. What is the sum?

  1. A Rs. 5,000
  2. B Rs. 4,000
  3. C Rs. 6,400
  4. D Rs. 8,000
Show answer and explanation

Correct answer: A - Rs. 5,000

For 2 years, the difference between compound and simple interest equals P x (r/100)^2. Here (r/100)^2 = (8/100)^2 = 0.0064. So P x 0.0064 = 32, giving P = 32 / 0.0064 = 5000. Checking: SI for 2 years = 5000 x 8 x 2/100 = 800; CI = 5000(1.08^2 - 1) = 5000 x 0.1664 = 832; difference = 32. Correct.

Q6
medium

The difference between the compound interest and the simple interest on a certain sum for 2 years at 8% per annum is Rs. 40. What is the principal sum?

  1. A Rs. 5,000
  2. B Rs. 6,250
  3. C Rs. 6,400
  4. D Rs. 5,500
Show answer and explanation

Correct answer: B - Rs. 6,250

For 2 years, the difference between compound and simple interest equals P x (r/100)^2. So 40 = P x (8/100)^2 = P x 0.0064. Therefore P = 40 / 0.0064 = Rs. 6,250.

Q7
medium

On a certain sum at 5% per annum, what is the difference between the compound interest (compounded annually) and the simple interest for 3 years, if the sum is Rs. 8,000?

  1. A Rs. 41
  2. B Rs. 61
  3. C Rs. 80
  4. D Rs. 121
Show answer and explanation

Correct answer: B - Rs. 61

Simple interest = 8000 x 5 x 3 / 100 = 1200. For compound interest, amount = 8000 x (1.05)^3 = 8000 x 1.157625 = 9261, so CI = 1261. Difference = 1261 - 1200 = 61. (The standard 3-year formula P x r^2 x (300 + r)/10^6 = 8000 x 25 x 305 / 1000000 = 61 confirms this.)

Q8
hard

A sum of Rs. 6,300 is borrowed at 10% per annum compound interest and is to be repaid in two equal annual installments. What is the amount of each installment?

  1. A Rs. 3,465
  2. B Rs. 3,630
  3. C Rs. 3,780
  4. D Rs. 3,150
Show answer and explanation

Correct answer: B - Rs. 3,630

Let each installment be X. The present value of the two installments must equal the loan. So X/1.1 + X/(1.1)^2 = 6300. Multiplying through: X(1.1 + 1)/(1.21) = 6300, i.e., X x (2.1/1.21) = 6300. Thus X = 6300 x 1.21 / 2.1 = 7623 / 2.1 = 3630. Each installment is Rs. 3,630.

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