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

The simple interest on a certain sum at the end of three years at 5%p.a. is Rs.1,200. The compound interest on the same sum for the same period at the same rate is (interest compounded yearly):

  1. Rs. 1,800

  2. Rs. 1,261

  3. Rs. 820

  4. Rs. 1,260
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The correct answer is Rs. 1,261 (Option B). First, find the principal using simple interest: SI = P × R × T / 100, so 1200 = P × 5 × 3 / 100, giving P = 1200 × 100 / 15 = Rs. 8000. For compound interest compounded yearly for 3 years at 5%: Amount = 8000 × (1.05)³ = 8000 × 1.157625 = Rs. 9261. Compound Interest = Amount - Principal = 9261 - 8000 = Rs. 1261. The difference between CI and SI is Rs. 61 (1261 - 1200).

Multiple choice

Rs 260200 is divided between Ram and Shyam so that the amount that Ram receives in 3 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Rams share (approx) is?

  1. 125000

  2. 137745

  3. 152000

  4. 108200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Ram's share be R, Shyam's share be S = 260200 - R. After compound interest: R(1.04)³ = S(1.04)⁶ = (260200 - R)(1.04)⁶. This gives R = (260200 - R)(1.04)³. Solving: R = 260200(1.04)³/[1 + (1.04)³] ≈ 137745.

Multiple choice

Abhi invested an amount of Rs A for 2 years at 12% compound interest and received some amount of interest. Sonali invested Rs (A + 1500) for 3 years at 8% simple interest and received same amount of interest as Abhi received. Find the amount that is invested by Abhi.

  1. ₹20000

  2. ₹25000

  3. ₹27500

  4. ₹25550
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Abhi's CI (compound interest): A[1.12² - 1] = A[1.2544 - 1] = 0.2544A. Sonali's SI (simple interest): (A+1500)×3×0.08 = 0.24(A+1500). Equating: 0.2544A = 0.24A + 360. Solving: 0.0144A = 360, giving A = 36000/1.44 = 25000.

Multiple choice

A certain principal at certain rate of simple interest for certain time gives a certain interest. The principal is increased by 30%, rate is made 80% of the previous rate and time duration is made 140% of the previous. In this way, the simple interest received is Rs.910. What is the difference of interest received in the first condition to the interest received at second condition?

  1. Rs.285

  2. Rs.254

  3. Rs.135

  4. Rs.235
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let original principal P, rate R, time T. Original interest I = P×R×T/100. New values: 1.3P, 0.8R, 1.4T. New interest = 1.3×0.8×1.4×I = 1.456I. Given new interest = Rs.910, so I = 910/1.456 = 625. Difference = 910 - 625 = 285.

Multiple choice

Sachin lent Rs 20000 to Ankit at simple interest at the rate of 10 per annum for 2 years and Ankit lent half of the money to Gaurav at simple interest at the rate of 15 per annum for 2 years and lent rest half of the money to Amar at compound interest at the rate of 5% per annum for 2 years Find the profit loss of Ankit after 2 years in the whole transaction.

  1. 25 loss

  2. 25 profit

  3. 35 loss

  4. 35 profit
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ankit's total payment to Sachin after 2 years is Rs 20000 + (20000 × 10% × 2) = Rs 24000. He lends Rs 10000 to Gaurav and receives 10000 + (10000 × 15% × 2) = Rs 13000. He lends Rs 10000 to Amar at compound interest and receives 10000 × (1.05)² = Rs 11025. Total received = Rs 24025. Profit = 24025 - 24000 = Rs 25.

Multiple choice

A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a., compounded annually, and each instalment is Rs. 5,808, then the total interest charged in this scheme is:

  1. 1536

  2. 1524

  3. 1520

  4. 1530
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Each instalment of Rs. 5,808 covers both principal and interest. Working backwards: Present value of second instalment = 5808 ÷ 1.1 = 5280. This leaves 5808 - 5280 = 528 as interest in year 2. Present value of first instalment = 5808 ÷ 1.1² = 5808 ÷ 1.21 = 4800. Total loan = 5280 + 4800 = 10080. Total repayment = 5808 × 2 = 11616. Interest = 11616 - 10080 = 1536. The discounting method accounts for compound interest.

Multiple choice

Anamika paid Rs. 4,965 as compound interest on a loan of Rs. 15,000 after 3 years when compounded annually. Suman took a loan of Rs. 10,000 at the same rate on simple interest. How much interest did Suman pay after 3 years?

  1. 3500

  2. 3000

  3. 4500

  4. 4000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For compound interest: 4965 = 15000[(1+r)^3 - 1], which gives (1+r)^3 = 1.331, so r = 10%. Simple interest at same rate for 3 years on Rs 10000: SI = 10000 × 10 × 3 / 100 = 3000. The key insight is that the rate must be found first from the compound interest case, then applied to simple interest.

Multiple choice

Two equal sums were lent on simple interest at 6% and 10% per annum respectively. The first sum was recovered two years later than the second sum and the amount in each case was Rs.1105. What was the sum (in Rs.) lent in each scheme?

  1. 891

  2. 745

  3. 850

  4. 900
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sum be P. For second loan at 10% for t years: Amount = P(1 + 10t/100) = 1105. For first loan at 6% for (t+2) years: Amount = P(1 + 6(t+2)/100) = 1105. Equating: P(1 + 0.1t) = P(1 + 0.06t + 0.12), which gives 0.1t = 0.06t + 0.12, so 0.04t = 0.12, meaning t = 3 years. Substituting: P(1 + 0.3) = 1105, so P = 1105/1.3 = 850. The key insight is that equal amounts from different rates and times must satisfy the equation.

Multiple choice

A sum of Rs.5000 is lent at two parts in such a way that first part at 4% and second at 5% per annum. If total interest received after two years is 440. Find the sum lent at 4%

  1. 3000

  2. 3125

  3. 3220

  4. 3020
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let 4% amount = x, then 5% amount = 5000 - x. Total interest: x×0.04×2 + (5000-x)×0.05×2 = 440. Simplifying: 0.08x + 0.1(5000-x) = 440. 0.08x + 500 - 0.1x = 440. -0.02x = -60; x = 3000. Verify: 3000×4%×2 + 2000×5%×2 = 240 + 200 = 440.