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

Rs. 16820 is divided between two brothers of age 27 years and 25 years. They invested their money at 5% per annum compound interest in such a way that both will receive equal money at the age of 40 years. Find the share of elder brother?

  1. 8280

  2. 8820

  3. 8000

  4. 8410
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the shares be A (27-year-old) and B (25-year-old), with A + B = 16820. At 5% compound interest, after (40-27)=13 years A becomes A(1.05)^13, and after (40-25)=15 years B becomes B(1.05)^15. For equal amounts at age 40: A(1.05)^13 = B(1.05)^15, giving A/B = (1.05)^2 = 1.1025. Solving A + B = 16820 and A = 1.1025B gives 2.1025B = 16820, B = 8000, A = 8820. The elder brother (27-year-old) gets 8820. Option B is correct.

Multiple choice

On a certain rate of interest a sum of Rs 5000 becomes Rs 16,200 in certain years at compound interest. In half of the time given, this sum will become?

  1. Rs. 10000

  2. Rs. 5600

  3. Rs. 9000

  4. Can not be determine

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

If amount grows from 5000 to 16200 in n years, the growth factor is 16200/5000 = 3.24. In half the time (n/2 years), the amount will be 5000 × sqrt(3.24) = 5000 × 1.8 = 9000. This uses the compound interest property that amount doubles by the square root of the growth factor when time is halved.

Multiple choice

If the difference between the compound interest (compounded annually) and the simple interest accrued in one and a half years at 8% per annum is Rs.80. What is the simple interest in three years on the same amount and at the same rate of interest?

  1. Rs.6000

  2. Rs.7200

  3. Rs.5600

  4. Rs.4800

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

For the difference between CI and SI in 1.5 years at 8%: CI - SI = P[(1.08)^1.5 - 1] - P(0.08)(1.5) = P(1.1232 - 1) - 0.12P = 0.1232P - 0.12P = 0.0032P = 80, so P = 25000. Simple interest for 3 years = 25000 × 0.08 × 3 = 6000.

Multiple choice

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 10,000 after 2 years at the same rate?

  1. Rs.2450

  2. Rs.2100

  3. Rs.1855

  4. Rs.2200

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

50% increase in 5 years at simple interest means the rate is 50%/5 = 10% per year. For compound interest on Rs. 10,000 at 10% for 2 years: Year 1 interest = Rs. 1,000, new principal = Rs. 11,000. Year 2 interest = 10% of Rs. 11,000 = Rs. 1,100. Total compound interest = Rs. 1,000 + Rs. 1,100 = Rs. 2,100.

Multiple choice

On a certain sum of money, after 2 years on the same rate simple interest and compound interest obtained are Rs 1200 and Rs 1500 respectively. What is the sum of money invested?

  1. 1500

  2. 1800

  3. 1200

  4. 1600

  5. 1400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For simple interest: SI = P×R×2/100 = 1200, so PR/100 = 600. For compound interest after 2 years: CI = P[(1+R/100)²−1] = 1500. The difference CI−SI = P(R/100)² = 300. Substituting PR = 60000 gives R = 50%, then P = 1200. The key insight is that the difference between CI and SI for 2 years equals P×R²/10000.

Multiple choice

Vinod borrows 4000 rupees at 10\% compound interest. At the end of every year, he pays back 1000 rupees. How much amount should he pay at the end of the third year to clear all his debt?

  1. 3014

  2. 2024

  3. 3814

  4. 3224

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

After each year, the outstanding amount grows by 10% compound interest, then 1000 is paid. Year 1: 4000 × 1.10 = 4400 - 1000 = 3400. Year 2: 3400 × 1.10 = 3740 - 1000 = 2740. Year 3: 2740 × 1.10 = 3014, which is the final payment to clear the debt.

Multiple choice

The simple interest accrued on Rs 36000 at the end of three years is Rs. 12000.What would be compound interest accrued on the same amount for same time period.(Approx.)

  1. 13380

  2. 13570

  3. 14250

  4. 13940

  5. 13900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple interest for 3 years is 12000 on 36000, so annual interest is 4000. Rate = 4000/36000×100 = 11.11%. Compound interest for 3 years at 11.11%: 36000×(1.1111³-1) = 36000×0.3717 = 13381 (approximately). Option A (13380) is closest.

Multiple choice

If a certain sum becomes 4 times in a 8 years at compound interest. Then in how many years, it will become 256 times?

  1. 16 year

  2. 32 year

  3. 40 year

  4. 26 year

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

If sum becomes 4 times in 8 years, then 4 = (1 + R)^8, so (1+R) = 4^(1/8) = 2^(1/4) = √√2. To become 256 times: 256 = (1+R)^n = 2^(n/4). Since 256 = 2^8, we get n/4 = 8, so n = 32 years. Alternatively: 4 times in 8 years means doubling every 4 years (since 2^2 = 4). To reach 256 = 2^8, we need 8 doublings, which takes 8 × 4 = 32 years.

Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer Quantity I- the difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% pa is Rs192. Find the principle amount. Quantity II- A sum fetched a total simple interest of Rs 9000 at the rate of 6% pa in 5 years. What is the sum?

  1. Quantity I > Quantity II

  2. Quantity I< Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

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

Quantity I: For 2 years at 8%, CI - SI = P(1.08² - 1) - P(0.08 × 2) = P(1.1664 - 1 - 0.16) = 0.0064P = 192. So P = 192/0.0064 = 30000. Quantity II: SI = P × R × T = P × 0.06 × 5 = 9000, so P = 9000/0.3 = 30000. Both quantities equal 30000. Option E stating they're equal is correct.

Multiple choice

A Sum of Rs 7140 is to be divided between Anita and Aman who are respectively 18 and 19 year old, in such a way that if there shares will be invested at 4% per annum at compound interest, they will receive equal amounts on attaining the age of 21 year. The present share of Anita is -

  1. 4225

  2. 4352

  3. 3500

  4. 4000

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

Let Anita's share = x, Aman's share = 7140 - x. Anita invests for 3 years (18 to 21), Aman for 2 years (19 to 21). At 4% CI with equal maturity amounts: x(1.04)^3 = (7140 - x)(1.04)^2. Divide both sides by (1.04)^2: x(1.04) = 7140 - x. So 1.04x + x = 7140, 2.04x = 7140, x = 7140/2.04 = 3500. Anita's present share is Rs 3500.