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 accured on an amount of Rs. 25,000 at the end of three years is Rs. 7,500 .What would be the compound interest accured on the same amount at the same rate in the same period?

  1. Rs. 7,750

  2. Rs. 8500

  3. Rs. 8275

  4. Rs. 8250
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest (SI) for 3 years on Rs. 25,000 is Rs. 7,500. Rate = (SI × 100) / (P × T) = (7500 × 100) / (25000 × 3) = 750000 / 75000 = 10% per annum. For Compound Interest (CI), Amount = P(1 + r/100)³ = 25000(1 + 10/100)³ = 25000(1.1)³ = 25000 × 1.331 = Rs. 33,275. CI = Amount - Principal = 33275 - 25000 = Rs. 8,275. The difference between CI and SI occurs because CI earns interest on accumulated interest, while SI is only on principal. Option A (Rs. 7,750) is close but incorrect. Option B (Rs. 8,500) and D (Rs. 8,250) don't match the calculation.

Multiple choice

What is the rate of interest p.c.p.a.? (I) Difference between compound interest and simple interest for 2 years is Rs. 125. (II) The amount doubles itself in 8 years on simple interest. (III) The amount invested is Rs. 12500.

  1. Only I

  2. Only I and III

  3. Either only II or I and III

  4. Either I and II or I and III

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

For interest rate problems: Statement II alone gives rate from doubling time (Simple Interest: if amount doubles in 8 years, rate = 100/8 = 12.5%). Statement I gives CI-SI difference formula involving rate and principal. Statement III gives principal. So either only II suffices, or I+III together (principal from III, then rate from CI-SI formula in I). This matches option C.

Multiple choice

What will be simple interest on an amount of Rs. 6351 at the rate of 5 p.c.p.a. after 7 years?

  1. Rs. 2208.55

  2. Rs. 2282.25

  3. Rs. 2525.85

  4. Rs. 2222.85

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

Simple Interest = Principal × Rate × Time / 100 = 6351 × 5 × 7 / 100 = 6351 × 35 / 100 = 222285 / 100 = Rs. 2222.85. Option D is correct. Option A (2208.55) is close but incorrect, Option B (2282.25) uses wrong calculation, and Option C (2525.85) is also miscalculated.

Multiple choice

A certain sum at a certain rate of simple interest to Rs. 1125 in 4 years and Rs. 1200 in 7 years. Find the rate of interest?

  1. 2.43%

  2. 3.62%

  3. 4%

  4. 5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest for 3 years (from year 4 to 7) = 1200 - 1125 = 75. Annual interest = 75/3 = 25. Principal = Amount after 4 years - Interest for 4 years = 1125 - 100 = 1025. Rate = (Annual Interest / Principal) × 100 = (25/1025) × 100 = 2.43%. Option B (3.62%), C (4%), and D (5%) are too high.

Multiple choice

What is the compound interest on Rs. 6000 at 10% per annum for one year compounded half yearly?

  1. Rs. 1260

  2. Rs. 630

  3. Rs. 615

  4. Rs. 600
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For half-yearly compounding at 10% per annum, the half-yearly rate is 5% per half-year. In one year (2 half-years): Amount = 6000 × (1.05)² = 6000 × 1.1025 = Rs. 6615. Compound Interest = 6615 - 6000 = Rs. 615. Option A (Rs. 1260) would be 21% simple interest, wrong rate. Option B (Rs. 630) is 10.5% simple interest, wrong compounding. Option D (Rs. 600) is exactly 10% simple interest, ignoring compounding.

Multiple choice

Rs. 600 becomes Rs. 708 in 3 years at a certain simple rate of interest. If the rate of interest is increased by 5%, what amount will Rs. 600 become in 3 years?

  1. Rs. 758

  2. Rs. 798

  3. Rs. 804

  4. Rs. 850

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

Interest earned = 708 - 600 = Rs. 108 in 3 years. Original rate = (108 × 100) / (600 × 3) = 6% p.a. New rate = 6 + 5 = 11%. New interest = (600 × 11 × 3) / 100 = Rs. 198. New amount = 600 + 198 = Rs. 798.

Multiple choice

Ravi invested Rs. 15000 at the rate of interest 10% p.a. for one year. If the compound interest is compounded every six months, what amount will Ravi get at the end of the year?

  1. Rs. 16537.50

  2. Rs. 16500

  3. Rs. 16525.50

  4. Rs. 18150
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Principal = Rs. 15000, Rate = 10% p.a., compounded half-yearly means rate per period = 5% and there are 2 periods. After first 6 months: Amount = 15000 × (1 + 5/100) = 15000 × 1.05 = Rs. 15750. After second 6 months: Amount = 15750 × 1.05 = Rs. 16537.50. Using formula: A = P(1 + r/200)^(2n) = 15000(1 + 10/200)² = 15000(1.05)² = 15000 × 1.1025 = 16537.50.

Multiple choice

A sum of money was invested at a certain rate of simple interest for 2 years. Had it been invested at 1% higher rate, it would have fetched Rs 24 more interest. The sum of money is :

  1. Rs 1200

  2. Rs 1050

  3. Rs 1000

  4. Rs 9600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For simple interest, extra interest earned at a higher rate = Principal × Extra Rate × Time. Here, Rs 24 = P × 1% × 2 years = P × 0.01 × 2. Therefore, P = 24 / 0.02 = Rs 1200. This is a straightforward application of the simple interest formula.

Multiple choice

What will be compound interest on a sum of Rs. 9000 at 4% per annum in 3 years? (two place of decimal)

  1. Rs.1143.77

  2. Rs.1223.77

  3. Rs.1123.77

  4. Rs.1133.77

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

Compound interest formula: A = P(1 + r/100)^n. Here P = Rs. 9000, r = 4%, n = 3. A = 9000(1.04)^3 = 9000 × 1.124864 = Rs. 10123.77. Compound Interest = A - P = 10123.77 - 9000 = Rs. 1123.77. Option C matches this calculation. The other options are either higher or lower than the correct value.

Multiple choice

Veena got a simple interest of Rs. 8376 on a certain amount at the rate of 8 p.c.p.a. for 6 years. How much amount did she invest?

  1. Rs. 17180

  2. Rs. 18110

  3. Rs. 16660

  4. Rs. 17450

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

Simple Interest = P × R × T / 100. Given SI = 8376, R = 8%, T = 6 years. So 8376 = P × 8 × 6 / 100 = 48P/100. Therefore P = 8376 × 100 / 48 = Rs. 17450. Options A, B, and C are calculation errors - using wrong multiplication or division.

Multiple choice

What is the annual instalment to discharge a debt of Rs. 2210 due in 4 years at 7% simple interest?

  1. 400 Rs.

  2. 500 Rs.

  3. 600 Rs.

  4. 450 Rs.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let each annual instalment be Rs. x. The first instalment is paid after 1 year and earns interest for 3 years, the second for 2 years, third for 1 year, and fourth for 0 years. Using the formula for sum of instalments with simple interest: x(1 + 3×0.07) + x(1 + 2×0.07) + x(1 + 0.07) + x = 2210. This gives x(1.21 + 1.14 + 1.07 + 1) = 2210, so x(4.42) = 2210, hence x = 500. Each instalment is Rs. 500.

Multiple choice

Rs. 800 amounts to Rs. 920 in 3 years at simple interest .If the interest rate in increased by 3% it would amount to -

  1. 1056 Rs.

  2. 1112 Rs.

  3. 1182 Rs.

  4. 992 Rs.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First find the original rate: Simple interest = 920 - 800 = 120 over 3 years, so annual interest = 40. Rate = (40/800) × 100 = 5% per annum. If rate increases by 3%, new rate = 8%. New interest for 3 years = 800 × 0.08 × 3 = 192. New amount = 800 + 192 = 992. The key is finding the original rate first, then applying the increased rate.

Multiple choice

If the difference between the compound interest and the simple interest on a certain sum for 2 years at 8% per annum is Rs. 32, the sum is -

  1. Rs. 5000

  2. Rs. 5220

  3. Rs. 5500

  4. Rs. 6000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 2 years at 8%, difference between CI and SI = P × (r/100)². Here: 32 = P × (8/100)² = P × 64/10000 = P/156.25. So P = 32 × 156.25 = Rs. 5000. Formula: Difference = P(r/100)² for 2 years. Option A (Rs. 5000) is correct. Simple interest for 2 years at 8% = 16% of P, compound interest = 16.64% of P, difference = 0.64% of P.