SSC CGL (Prelims) General: Compound Interest questions with solutions

Q1. Find the compound interest on ₹12,000 at 8% per annum for 2 years 6 months, compounded annually.

1. ₹ 2,000
2. ₹ 2,140.8
3. ₹ 2,556.67
4. ₹ 2,500

Answer: ₹ 2,556.67

For annual compounding, first calculate amount after 2 years: \(12000\times1.08^2=13996.8\). For the remaining 6 months, add simple interest at 8% for half a year on this amount: \(13996.8\times0.04=559.872\). Thus total CI \(=13996.8+559.872-12000=2556.672\approx ₹2556.67\).

Q2. A certain amount invested at 15% compound interest per annum, compounded annually, becomes ₹4,235 in 2 years. What is 120% of the principal?

1. ₹ 3,080
2. ₹ 3,200
3. ₹ 3,500
4. ₹ 3,840

Answer: ₹ 3,840

If the amount after 2 years at 15% compound interest is ₹4235, then \(P(1.15)^2=4235\). So \(P=4235/1.3225=3200\). Therefore, 120% of the principal is \(1.2\times3200=3840\).

Q3. A sum of ₹8000 amounts to ₹9245 in 2 years at compound interest, compounded annually. What is the annual rate of interest?

1. 6.5%
2. 7%
3. 7.5%
4. 8%

Answer: 7.5%

For annual compounding, \(A=P(1+r/100)^2\). Here \(\frac{9245}{8000}=1.155625\), so \((1+r/100)^2=1.155625\). Taking square root gives \(1+r/100=1.075\), hence \(r=7.5\%\).

Q4. A certain amount triples its initial value after 8 years of compound interest. How many years will it take to grow to eighty-one times its original amount?

1. 24
2. 30
3. 32
4. 36

Answer: 32

If the amount triples in 8 years, then after 8 years the factor is 3. To become 81 times, we need 81 = 3^4, so it takes 4 such periods. Therefore, the total time is 4 × 8 = 32 years.

Q5. A sum of money invested at compound interest amounts to three times itself in 5 years. In how many years will it become 27 times itself?

1. 12 years
2. 15 years
3. 18 years
4. 20 years

Answer: 15 years

If the money becomes 3 times in 5 years, then every 5 years it is multiplied by 3. To become 27 times, we need $27=3^3$, i.e., three such periods. Hence, time required is $3\times 5=15$ years.

Q6. A businessman invests Rs. 85,000 at a rate of 10% compound interest per annum, compounded annually. Find the interest for the 3rd year only.

1. Rs. 10,285
2. Rs. 9,350
3. Rs. 8,500
4. Rs. 11,250

Answer: Rs. 10,285

For compound interest, the interest in a particular year is calculated on the amount accumulated up to the previous year. After 2 years, the amount is 85,000 × 1.1² = 102,850, so the 3rd-year interest is 10% of this, i.e. 10,285.

Q7. A certain sum amounts to Rs. 1,600 in two years and to Rs. 2,000 in three years at compound interest compounded annually. Find the rate of interest.

1. 21%
2. 19%
3. 25%
4. 20%

Answer: 25%

With annual compounding, the amount in year 3 is the year 2 amount multiplied by $1+r$. So $2000/1600 = 1.25$, giving $r = 0.25 = 25\%$.

Q8. An amount of ₹8,000 is invested at a compound interest rate of 10% per annum for 2 years. What is the total amount received?

1. ₹ 9,600
2. ₹ 9,680
3. ₹ 9,720
4. ₹ 10,000

Answer: ₹ 9,680

For compound interest, \(A = P(1 + r/100)^n\). Here \(P=8000\), \(r=10\), and \(n=2\), so \(A = 8000 \times 1.1^2 = 8000 \times 1.21 = 9680\).

Q9. If the amount is Rs. 600 and the principal is Rs. 450, compounded yearly for 1 year, calculate the rate of interest.

1. 40%
2. 45%
3. 33.33%
4. 35%

Answer: 33.33%

For 1 year, the compound interest formula becomes $A=P\left(1+\frac{R}{100}\right)$. Here, interest = 600 - 450 = 150. So $150 = 450\cdot \frac{R}{100}$, giving $R = 33.33\%$.