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

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (Only quantity is to be considered) Find the principal . Quantity I :- If the difference between compound interest and simple interest at 12 % per annum in 2 years is 1296 . Quantity II :- If the compound interest of two years, at the rate in which a sum of Rs 512 becomes Rs 729 in 3 years , is Rs 21250 .

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: CI - SI difference formula for 2 years at r% is P × (r/100)². Given 1296 = P × (12/100)² = P × 0.0144, so P = 1296/0.0144 = Rs 90,000. Quantity II: Rs 512 becomes Rs 729 in 3 years. Growth factor = 729/512 = (9/8)³ = 1.4238, meaning annual rate = 12.5%. CI for 2 years at 12.5% on principal P: P × [(1.125)² - 1] = 21250. So P × 0.265625 = 21250, giving P = Rs 80,000. Since 90,000 > 80,000, Quantity I > Quantity II.

Multiple choice

Any sum invested for 3.5 years at 12% annual interest, at maturity becomes Rs. 994. What was the original amount invested?

  1. Rs. 700

  2. Rs. 750

  3. Rs. 725

  4. Rs. 720
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the simple interest formula A = P(1 + rt), where A is the maturity amount, P is the principal, r is the annual rate, and t is time in years. Given A = Rs. 994, r = 12% = 0.12, and t = 3.5 years: 994 = P(1 + 0.12 × 3.5) = P(1 + 0.42) = 1.42P. Therefore, P = 994/1.42 = Rs. 700.

Multiple choice

The difference between the compound interest on a certain sum for the second year and the third year at 5% p.a. is Rs.42. Find the sum.

  1. Rs. 12000

  2. Rs. 15000

  3. Rs. 16000

  4. Rs. 20000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For compound interest, the CI for the second year on principal P at 5% is P(1.05)² - P(1.05) = P(0.05)(1.05). The CI for the third year is P(1.05)³ - P(1.05)² = P(0.05)(1.05)². The difference is P(0.05)(1.05)² - P(0.05)(1.05) = P(0.05)(1.05)(1.05 - 1) = P(0.05)(1.05)(0.05) = 0.002625P. Given this difference is Rs. 42, we have 0.002625P = 42, so P = 42/0.002625 = Rs. 16,000.

Multiple choice

The difference between the interests earned when Rs. P is invested for four years in a scheme offering 9% p.a. Simple interest and when the same sum (Rs P) is invested for two years in another scheme offering 12% p.a. Compound interest, is Rs 528. What is the value of P?

  1. 4000

  2. 5000

  3. 4500

  4. 3500

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

Simple Interest for 4 years at 9% = P × 9 × 4 / 100 = 0.36P. Compound Interest for 2 years at 12% = P(1 + 12/100)^2 - P = P(1.12)^2 - P = 0.2544P. The difference is 0.36P - 0.2544P = 0.1056P = 528. Solving: P = 528/0.1056 = 5000.

Multiple choice

A sum of money was invested for “X” years in scheme A offering simple interest. The amount received after “X” years was twice the sum of money invested in the scheme. What will be the amount received from scheme A, when a sum of Rs 2800, is invested for “2X” years.

  1. 11200

  2. 5600

  3. 8400

  4. 9600

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

If amount after X years is twice the principal, then interest equals principal. In simple interest, if I = P in X years, then the rate r = 100/X %. For 2X years, the interest will be 2P (double the time). When Rs 2800 is invested for 2X years, interest = 2 × 2800 = Rs 5600. Amount = Principal + Interest = 2800 + 5600 = Rs 8400. This is option C.

Multiple choice

Aman lent Rs 21600 to Sangram for 3 years and Rs 15000 to Pramod for 2 years on simple interest at the same rate of interest and received Rs 2844 in all from both of them as interest. The rate of interest per annum is:

  1. 3.5%

  2. 4%

  3. 3%

  4. 4.5%

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

Using SI = PRT/100 for both loans: For Sangram: 21600 x R x 3 / 100 = 648R. For Pramod: 15000 x R x 2 / 100 = 300R. Total interest = 648R + 300R = 948R = 2844. Solving: R = 2844/948 = 3. The rate is 3% per annum. The key is adding the interest amounts and solving for the common rate R.

Multiple choice

What is the ratio of the simple interest earned by certain amount for 4 years and 7 years at the same rate of interest?
  1. $4 : 7$
  2. $3 : 7$
  3. $2 : 3$
  4. $5 : 7$

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

Simple interest is directly proportional to time when principal and rate are constant. For the same principal P and rate R, SI for 4 years = 4PR/100 and SI for 7 years = 7PR/100. The ratio SI(4 years):SI(7 years) = 4PR:7PR = 4:7. Time is the only variable.

Multiple choice

P & Q amounts equal that is Rs. 12,000. P invested half of the amount at 10% CI & remaining at 6% of SI for 2 years and Q invested (\frac{3}{4}) amount at 20% CI & remaining at 10% SI for 2 years. Find the interest received by P & Q both ?

  1. 4650

  2. 5460

  3. 6450

  4. 6540

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

P invests half (6000) at 10% CI for 2 years: 6000(1.1)² - 6000 = 6000 × 1.21 - 6000 = 7260 - 6000 = 1260. Remaining 6000 at 6% SI for 2 years: 6000 × 0.06 × 2 = 720. P's total interest = 1260 + 720 = 1980. Q invests 3/4 (9000) at 20% CI for 2 years: 9000(1.2)² - 9000 = 9000 × 1.44 - 9000 = 12960 - 9000 = 3960. Remaining 3000 at 10% SI for 2 years: 3000 × 0.10 × 2 = 600. Q's total interest = 3960 + 600 = 4560. Combined interest = 1980 + 4560 = 6540.

Multiple choice

A invested Rs 14400 for 3 years at 10% per annum simple interest. If he invested the same amount for 1.5 years when interest rate is same but compounded half yearly. Find the difference between the interests.
  1. $2050.2$
  2. $2250.0$
  3. $1872.2$
  4. $2150.0$

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

SI = 14400 x 0.1 x 3 = Rs 4320. For CI: rate 10% compounded half-yearly means 5% per period for 3 periods in 1.5 years. CI = 14400[(1 + 0.05)^3 - 1] = 14400[1.157625 - 1] = Rs 2269.8. Difference = 4320 - 2269.8 = Rs 2050.2. Half-yearly compounding increases periods but reduces rate per period.

Multiple choice

If difference between simple interest on a certain sum at 4% for 6 years and compound interest on the same sum at 5% for 3 years is Rs. 1647.5. Find the sum.

  1. Rs. 12000

  2. Rs. 15000

  3. Rs. 18000

  4. Rs. 16000

  5. Rs. 20000
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Simple Interest at 4% for 6 years: SI = P×4×6/100 = 0.24P. Compound Interest at 5% for 3 years: CI = P(1.05³-1) = P(1.157625-1) = 0.157625P. Given: 0.24P - 0.157625P = 1647.5, so 0.082375P = 1647.5, P = 1647.5/0.082375 ≈ 20000. The difference formula is key - SI uses simple multiplication, CI uses compound interest factor.