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

Neha's Rs. 8000 in 3 years at a fixed simple interest rate becomes Rs. 9200. If the rate of interest was increased by 2%, what amount would he have received?

  1. Rs. 9680

  2. Rs. 8900

  3. Rs. 9800

  4. Rs. 2000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple interest earned = Rs. 9200 - Rs. 8000 = Rs. 1200 over 3 years. Rate = (1200 × 100) / (8000 × 3) = 5%. If rate increases by 2% to 7%, new interest = (8000 × 7 × 3) / 100 = Rs. 1680. Total amount = 8000 + 1680 = Rs. 9680.

Multiple choice

P and Q have equal amounts. P invested half amount at 10% compound interest and remaining half at 6% simple interest for 2 years and Q invest half amount at 20% compound interest and remaining amount at 10% simple interest for 2 years. If the total interest received by both P and Q is Rs 15080, find the approximate sum.

  1. 18500

  2. 32000

  3. 35000

  4. 31000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the amount be x. P: half at 10% CI (2yr) gives 0.5x[(1.1)²-1] = 0.5x(0.21) = 0.105x. Half at 6% SI (2yr) gives 0.5x×0.06×2 = 0.06x. Total P = 0.165x. Q: half at 20% CI gives 0.5x[(1.2)²-1] = 0.5x(0.44) = 0.22x. Half at 10% SI gives 0.5x×0.10×2 = 0.10x. Total Q = 0.32x. Combined interest: 0.165x + 0.32x = 0.485x = 15080. x = 15080/0.485 ≈ 31093, rounds to 31000.

Multiple choice

20000 rupees is kept at 18% compound interest rate (compounded annually). If interest is compounded half-yearly, how much more interest (in rupees) will be received?
  1. $486$
  2. $648$
  3. $162$
  4. $324$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Annual compounding: 20000 at 18% for 1 year = 3600 interest. Half-yearly: rate = 9% per half-period, amount after 2 periods = 20000 × 1.09 × 1.09 = 23762. Interest = 3762. Difference = 3762 - 3600 = 162. The half-yearly compounding yields 162 more interest, confirming option C.

Multiple choice

The simple interest of a certain sum of money is (\frac{16}{25}) of its principal. The number of years is equal to the interest rate per year. What is the interest rate (in percentage) per year?

  1. 4

  2. 16

  3. 8

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

Let principal = P, rate = r% per year, time = t years. Given: SI = (16/25)P and t = r. SI = P × r × t/100 = P × r × r/100 = Pr^2/100. So Pr^2/100 = 16P/25. r^2/100 = 16/25. r^2 = 16 × 100/25 = 64. r = 8% (since r cannot be negative). Verifying: SI = P × 8 × 8/100 = 64P/100 = 16P/25. Correct.

Multiple choice

If the simple interest on a sum of money for 2 years at 5% per annum is Rs 500, what is the compound interest (approximate) on the same at the same rate and for the same time?
  1. $508.25$
  2. $506.25$
  3. $512.5$
  4. $520.5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest for 2 years at 5% is Rs 500, so for 1 year it's Rs 250. Principal = 250/0.05 = Rs 5000. Compound Interest for 2 years at 5% on Rs 5000: Year 1 interest = 5000 x 0.05 = 250. Year 2 principal = 5250, interest = 5250 x 0.05 = 262.50. Total CI = 250 + 262.50 = 512.50. The claimed answer C is correct.

Multiple choice

Rs 5000 amounts to Rs 6920 in 4 years at a certain rate of interest. If the rate becomes 1.5 times to itself, the amount of the same principal in 5 years will be:

  1. Rs 6000

  2. Rs 7000

  3. Rs 8600

  4. Rs 9000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using compound interest formula: A = P(1 + r)^t. From 5000 to 6920 in 4 years: 6920/5000 = (1 + r)^4, so 1.384 = (1 + r)^4, giving r ≈ 0.084 or 8.4% annually. At 1.5 times rate = 12.6% for 5 years: 5000(1.126)^5 = 5000 × 1.805 = Rs 9025. This doesn't match. Using simple interest: (6920-5000)/(5000×4) = 1920/20000 = 9.6%. At 1.5× = 14.4% for 5 years: 5000 + 5000×0.144×5 = 5000 + 3600 = Rs 8600.

Multiple choice

The simple interest on a certain sum at the end of three years at 5% per annum is Rs 1200. The compound interest on the same sum for the same period at the same rate is (interest compounded annually):

  1. 1800

  2. 1261

  3. 820

  4. 1260
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest for 3 years at 5% is Rs 1200, so annual SI = 400. Since SI = P×R×T/100, we have 1200 = P×5×3/100, giving P = 8000. Compound interest for 3 years: P(1.05)³ - P = 8000(1.157625) - 8000 = 9261 - 8000 = 1261. Option B is correct. Option A (1800) is simple interest for different parameters. Option D (1260) is close but doesn't account for compounding properly.

Multiple choice

A borrows a sum of Rs 2000 from his friend B on 31st December 2011 on the condition that he will return the same after one year with simple interest at 8% per annum. However, A gets into a position of returning the money on 1 July 2012. How much amount he has to return to B?

  1. 2200

  2. 2080

  3. 2088

  4. 2070
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Principal = Rs 2000, Rate = 8% per annum. Time from Dec 31, 2011 to July 1, 2012 = 6 months = 0.5 years. Simple Interest = P × R × T = 2000 × 0.08 × 0.5 = Rs 80. Total amount = Principal + Interest = 2000 + 80 = Rs 2080.

Multiple choice

The simple interest obtained when a sum of money is invested for 4 years at 18% per annum is Rs 854 more than the simple interest obtained if the same sum of money invested for 2 years at 22% per annum. What is the amount obtained when the same sum of money invested for 4 years at 18% per annum?

  1. 4260

  2. 5246

  3. 2192

  4. 3708

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

Let principal = P. SI at 18% for 4 years = P × 18 × 4/100 = 0.72P. SI at 22% for 2 years = P × 22 × 2/100 = 0.44P. Difference = 0.72P - 0.44P = 0.28P = 854, so P = 3050. Amount = P + SI = 3050 + 0.72 × 3050 = 3050 + 2196 = 5246. Option B is correct.