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Quantitative Aptitude — Interest
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Quantitative Aptitude — Interest

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12 mins
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15
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1
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Quantitative Aptitude — Interest — Questions with Answers Open after you finish the quiz — all 15 questions, with answers and explanations.
Q1. A sum borrowed at 5% per annum simple interest earns an interest which is one-fourth of its principal in x years. Find x.
  1. 5 years
  2. 4 years
  3. 6 years
  4. 7 years
Show answer
Answer: A. 5 years
Given SI = P/4. Using SI = PRT/100, we get P/4 = (P × 5 × x)/100. So 100P = 20Px, hence x = 100/20 = 5 years.
Q2. What will Rs. 50,000 amount to in 2 years at the rate of 10% per annum, if interest is compounded yearly?
  1. Rs. 55,000
  2. Rs. 60,000
  3. Rs. 60,500
  4. Rs. 62,500
Show answer
Answer: C. Rs. 60,500
A = P(1 + R/100)^n = 50000 × (1 + 10/100)^2 = 50000 × (1.1)^2 = 50000 × 1.21 = 60,500.
Q3. How long will a sum of money take to double, if it is invested at 10% per annum simple interest?
  1. 8 years
  2. 9 years
  3. 10 years
  4. 12 years
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Answer: C. 10 years
For money to double, SI = P. So P = (P × 10 × T)/100, giving T = 100/10 = 10 years.
Q4. What is the ratio of simple interest earned on a certain amount at the rate of 8% per annum for 5 years and that for 10 years?
  1. 1:2
  2. 2:3
  3. 3:4
  4. 1:3
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Answer: A. 1:2
When Principal (P) and Rate (R) are the same, Simple Interest (SI) is directly proportional to time (T). So the ratio of interests will be the ratio of times: 5 : 10 = 1 : 2.
Q5. What will be the effective rate of interest if the annual rate is 12% and the interest is compounded on a half-yearly basis?
  1. 12.18%
  2. 12.36%
  3. 12.42%
  4. 12.50%
Show answer
Answer: B. 12.36%
Half-yearly rate becomes 12%/2 = 6%. Effective annual rate = [(1 + 6/100)^2 - 1] × 100 = [(1.06)^2 - 1] × 100 = (1.1236 - 1) × 100 = 12.36%.
Q6. A certain sum amounts to Rs. 20,000 in 5 years at x% per annum on simple interest. If the rate of simple interest per annum had been (x + 2)%, the amount payable after 5 years would have been Rs. 22,000. Find the sum invested.
  1. Rs. 18,000
  2. Rs. 19,000
  3. Rs. 20,000
  4. Rs. 21,000
Show answer
Answer: C. Rs. 20,000
The extra amount due to 2% higher rate over 5 years = 22000 - 20000 = 2000. So (P × 2 × 5)/100 = 2000, giving 10P/100 = 2000, hence P = 2000 × 100/10 = 20,000.
Q7. A sum of Rs. 10,000 was invested for a year at 8% per annum interest, compounded half-yearly. What would be the interest payable at the end of the year?
  1. Rs. 800
  2. Rs. 816
  3. Rs. 832
  4. Rs. 848
Show answer
Answer: B. Rs. 816
Half-yearly rate = 8%/2 = 4%, and time = 2 half-years. A = 10000 × (1 + 4/100)^2 = 10000 × (1.04)^2 = 10000 × 1.0816 = 10,816. Interest = 10816 - 10000 = 816.
Q8. The amount payable on maturity of a certain sum invested for 4 years at a certain rate per annum is Rs. 8,000, and the amount payable on the same sum invested for 6 years at the same rate is Rs. 10,000. If simple interest is offered in both cases, the rate of interest per annum is:
  1. 20%
  2. 22.5%
  3. 25%
  4. 30%
Show answer
Answer: C. 25%
Interest for extra (6-4) = 2 years = 10000 - 8000 = 2000. So SI for 1 year = 2000/2 = 1000. SI for 4 years = 4 × 1000 = 4000. Principal = Amount - SI = 8000 - 4000 = 4000. Now, SI = PRT/100 => 4000 = (4000 × R × 4)/100 => 4000 = 160R, hence R = 4000/160 = 25%.
Q9. A sum of money at a certain rate of interest when compounded annually becomes Rs. 800 in 2 years and Rs. 880 in 3 years. What is the rate of interest per annum?
  1. 8%
  2. 10%
  3. 12%
  4. 15%
Show answer
Answer: B. 10%
Interest earned during the 3rd year alone = 880 - 800 = 80. This interest is on the amount at the start of the 3rd year, which is 800. So Rate = (Interest / Principal for that year) × 100 = (80/800) × 100 = 10%.
Q10. A certain sum on compound interest becomes Rs. 48,400 when compounded annually after 2 years and Rs. 53,240 after 3 years. Find the sum.
  1. Rs. 40,000
  2. Rs. 42,000
  3. Rs. 44,000
  4. Rs. 45,000
Show answer
Answer: A. Rs. 40,000
CI in 3rd year = 53240 - 48400 = 4840. Rate = (4840/48400) × 100 = 10%. Now, A = P(1 + R/100)^n => 48400 = P × (1 + 10/100)^2 = P × (1.1)^2 = P × 1.21. So P = 48400 / 1.21 = 40,000.
Q11. Out of a total sum of Rs. 6,000, Danish invested one part at 8% simple interest per annum and the remaining part at 10% simple interest per annum. If the total interest that accrued to Danish in three years equals Rs. 1,620, what was the sum Danish invested at 8% simple interest per annum?
  1. Rs. 2,500
  2. Rs. 3,000
  3. Rs. 3,500
  4. Rs. 4,000
Show answer
Answer: B. Rs. 3,000
Let the part invested at 8% be x, then the part at 10% is (6000 - x). Total 3-year interest = (x × 8 × 3)/100 + ((6000-x) × 10 × 3)/100 = 1620. This simplifies to 0.24x + 1800 - 0.3x = 1620, so -0.06x = 1620 - 1800 = -180, hence x = 180 / 0.06 = 3,000.
Q12. The difference between the interest payable on a sum invested for three years at 10% compound interest per annum compounded annually and 10% simple interest per annum for the same period is Rs. 62. What is the value of the sum invested?
  1. Rs. 1,500
  2. Rs. 2,000
  3. Rs. 2,500
  4. Rs. 3,000
Show answer
Answer: B. Rs. 2,000
For 3 years at 10%, CI - SI = P × [(1 + 0.1)^3 - 1 - 3 × 0.1] = P × [1.331 - 1 - 0.3] = P × 0.031. So 62 = 0.031P, giving P = 62 / 0.031 = 2,000.
Q13. On what sum will the compound interest, at the rate of 10% per annum for 2 years compounded annually, be Rs. 2,100?
  1. Rs. 9,000
  2. Rs. 10,000
  3. Rs. 10,500
  4. Rs. 11,000
Show answer
Answer: B. Rs. 10,000
CI = P[(1 + R/100)^n - 1] = P[(1 + 10/100)^2 - 1] = P[(1.1)^2 - 1] = P[1.21 - 1] = 0.21P. So 2100 = 0.21P, giving P = 2100 / 0.21 = 10,000.
Q14. A principal amount of Rs. 8,000 borrowed at compound interest is raised to Rs. 9,261 in 3 years. What is the rate of interest?
  1. 4%
  2. 5%
  3. 6%
  4. 7%
Show answer
Answer: B. 5%
A/P = (1 + R/100)^n. So 9261/8000 = (1 + R/100)^3. We know that 9261 = 21^3 and 8000 = 20^3. So (21/20)^3 = (1 + R/100)^3. Taking cube root on both sides: 21/20 = 1 + R/100, hence R/100 = 21/20 - 1 = 1/20, so R = 5%.
Q15. A invests two equal amounts in two banks giving rates of simple interest as 8% per annum and 12% per annum respectively. At the end of the year, the total interest earned is Rs. 2,000. The amount invested in each bank is:
  1. Rs. 8,000
  2. Rs. 9,000
  3. Rs. 10,000
  4. Rs. 12,000
Show answer
Answer: C. Rs. 10,000
Let each amount be x. Then total interest = (x × 8 × 1)/100 + (x × 12 × 1)/100 = 0.08x + 0.12x = 0.20x. Given total interest = 2000. So 0.20x = 2000, which means x = 2000 / 0.20 = 10,000.
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