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

A merchant lent out Rs. 1000 in two parts, one at 8% and the other at 10% interest. The yearly average comes out to the 9.2%. Find the amount lent at 10% interest is -

  1. Rs. 450

  2. Rs. 400

  3. Rs. 600

  4. Rs. 650
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the amount lent at 10% be x. Then amount at 8% is (1000-x). Total interest = 0.08(1000-x) + 0.10x = 80 - 0.08x + 0.10x = 80 + 0.02x. Average rate = (80+0.02x)/1000 = 0.092, so 80+0.02x = 92, giving 0.02x = 12, x = 600. The 10% amount is Rs. 600.

Multiple choice

What annual installment will discharge a debt of Rs. 47250 for 3 years hence at the rate of 5% simple interest?

  1. Rs. 16050

  2. Rs. 14750

  3. Rs. 15000

  4. Rs. 15500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For annual installments under simple interest, each installment earns interest for the remaining period. Let annual installment = x. Total value: x(1 + 2×0.05) + x(1 + 1×0.05) + x = x(1.1 + 1.05 + 1) = 3.15x. This equals 47250, so x = 47250/3.15 = 15000. Verification: First installment earns 10% interest (2 years), second earns 5% (1 year), third earns nothing: 15000×1.1 + 15000×1.05 + 15000 = 16500 + 15750 + 15000 = 47250. Option A (16050) would give total 50557.5.

Multiple choice

Ravi borrowed some money at the rate of 4 p.c.p.a. for the first three years, at the rate of 8 p.c.p.a. for the next two years and at the rate of 9 p.c.p.a. for the period beyond 5 years. If he pays a total simple interest of Rs. 19,550/- at the end of 7 years, how much money did he borrow ?

  1. Rs. 39,500/-

  2. Rs. 42,500/-

  3. Rs. 41,900/-

  4. Rs. 43,000/-

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

Let principal be P. Total SI = P×4×3/100 + P×8×2/100 + P×9×2/100 = 12P/100 + 16P/100 + 18P/100 = 46P/100 = 19550. So P = 19550×100/46 = 42500. The calculation is straightforward: different rates apply to different time periods, and simple interest is calculated on the same principal throughout.

Multiple choice

At what rate percent compound interest per annum will Rs 640 amount to Rs 795.07 in 3 years?

  1. 7.5%

  2. 4.5%

  3. 7.0%

  4. 8.0%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use compound interest formula: A = P(1 + r/100)^t. Here 795.07 = 640(1 + r/100)^3. Solving: (1 + r/100)^3 = 795.07/640 = 1.2423. Taking cube root: 1 + r/100 = 1.075. Therefore r = 7.5%. Verify: 640 × 1.075^3 = 640 × 1.2423 ≈ 795.07. Options C and D are close but don't yield the exact amount.

Multiple choice

If the difference between the compound and simple interests on a certain sum of money for 3 years at 5% per annum is Rs. 15.25, then the sum is -

  1. Rs. 1600

  2. Rs. 2400

  3. Rs. 1820

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

Difference between CI and SI for 3 years at 5% is P[(1.05)³ - 1 - 0.15] = P[1.1576 - 1.15] = P(0.0076). Given difference is Rs. 15.25, so P = 15.25/0.0076 ≈ Rs. 2000. The formula for difference is: CI - SI = P[(1 + r/100)³ - 1 - 3r/100].

Multiple choice

What is the rate of interest p.c.p.a.? I. The amount becomes Rs 11025 at compound interest after 2 years. II. The same amount with simple interest becomes Rs 11000 after 2 years. III. The amount invested is Rs 10000.

  1. Only II and III

  2. Any two

  3. Only I and III

  4. Any one

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

We need to find the rate of interest per annum. Statement I: Amount after 2 years at CI is Rs 11025. Statement II: Amount after 2 years at SI is Rs 11000. Statement III: Principal is Rs 10000. Using I+III: 11025 = 10000(1 + r/100)^2, we can find r. Using II+III: 11000 = 10000 + 10000×r×2/100, giving r = 5%. Using I+II: The difference between CI and SI for 2 years on same principal gives the rate. Any two statements are sufficient to determine r.

Multiple choice

The difference between C.I. and S.I. on a certain sum of money at the rate of 5% per annum for three years is Rs. 190625 then find the difference between C.I. and S.I. for two years at the same rate of interest and same sum.

  1. Rs. 82500

  2. Rs. 25000

  3. Rs. 72500

  4. Rs. 62500

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

For 3 years at 5%, CI - SI = P[(1+r/100)³ - 1 - 3r/100] = P[(1.05)³ - 1 - 0.15] = P[1.157625 - 1 - 0.15] = P(0.007625). Given this equals 190625, so P = 190625/0.007625 = 25000000. For 2 years: CI - SI = P[(1.05)² - 1 - 0.10] = 25000000[1.1025 - 1 - 0.10] = 25000000(0.0025) = 62500. Or use direct formula: Difference for n years = P(r/100)²(n-1)/2 for first 2 years, but the 3-year formula gives us P, then apply for 2 years.

Multiple choice

The simple interest on Rs 10 for 4 months at the rate of 3 paise per rupee is -
  1. $Rs 1.20$
  2. $Rs 1.60$
  3. $Rs 2.40$
  4. $Rs 3.60$

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

Principal = Rs 10. Rate = 3 paise per rupee per annum = 3% per annum. Time = 4 months = 4/12 = 1/3 year. Simple Interest = P × R × T / 100 = 10 × 3 × (1/3) / 100 = 10 × 1 / 100 = Rs 0.10. Wait, this calculation gives Rs 0.10, not Rs 1.20. Let me recalculate: 3 paise per rupee means 3 paise on Rs 1 for the given period. If the rate is 3 paise per rupee for 4 months, then on Rs 10, the interest is 30 paise = Rs 0.30. But if the rate is 3 paise per rupee per annum, then for 4 months: SI = 10 × 3 × (1/3) / 100 = 0.10. Neither matches Rs 1.20. However, if the question means the rate is 3 paise per rupee per month (annualized to 36%), then SI = 10 × 36 × (1/3) / 100 = Rs 1.20. This interpretation gives option A.

Multiple choice

Nilima invested Rs 60,000 in a nationalised bank for 2 years at the rate of 8.5 p.c.p.a. at compound interest. What amount will Nilima receive from the bank at the end of 2 years?

  1. Rs 70433.5

  2. Rs 70200

  3. Rs 70933.5

  4. Rs 70633.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compound Interest formula: A = P(1 + r/100)ⁿ. Principal = Rs 60,000, rate = 8.5%, time = 2 years. A = 60000 × (1 + 8.5/100)² = 60000 × (1.085)² = 60000 × 1.177225 = Rs 70633.5. The compound amount after 2 years is Rs 70633.5.