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

Q1. The compound interest on a principal at 20% p.a. for 1.5 years, compounded annually, is ₹3,400. Find the principal.

1. ₹ 10,625
2. ₹ 12,000
3. ₹ 15,000
4. ₹ 18,150

Answer: ₹ 10,625

With annual compounding for 1.5 years, amount after 1 year is \(1.2P\). For the next half-year, simple interest at 20% p.a. on \(1.2P\) is \(0.1\times1.2P=0.12P\). Total CI is \(0.2P+0.12P=0.32P=3400\), giving \(P=10625\).

Q2. If the compound interest on a sum at $14\tfrac{2}{3}\%$ per annum for 3 years is ₹1,680, find the simple interest for the same period and rate.

1. ₹ 1,232
2. ₹ 1,456
3. ₹ 1,600
4. ₹ 1,812

Answer: ₹ 1,456

For 3 years, compound interest is $P\left[(1+r)^3-1\right]$, where $r=14\tfrac{2}{3}\%=\frac{11}{75}$. Using the given CI, we get the principal, and then simple interest for 3 years at the same rate comes out to ₹1,456.

Q3. In how many years will Rs. 80,000 become Rs. 1,06,480 at 10% compound interest per annum?

1. 3
2. 4
3. 5
4. 7

Answer: 3

Under compound interest, amount after n years is \(80000(1.1)^n\). Now \(80000\times1.1^3 = 80000\times1.331 = 106480\). Therefore, the required time is 3 years.

Q4. Find the compound interest on ₹9,500 at 11% p.a. for 2 years 6 months, compounded annually.

1. ₹ 2,848.72
2. ₹ 2,798.25
3. ₹ 2,850
4. ₹ 2,950.50

Answer: ₹ 2,848.72

For annual compounding, compute the amount after 2 years and then apply simple interest for the remaining 6 months on that amount. The difference between the final amount and principal gives the compound interest.

Q5. If the amount at the end of the 4th year and 5th year on a certain principal at compound interest is ₹24,000 and ₹26,400 respectively, find the rate of interest per annum.

1. 8%
2. 9%
3. 10%
4. 11%

Answer: 10%

In compound interest, successive yearly amounts differ by a constant factor of (1+r). The ratio 26400/24000 = 1.1, so the rate is 10% per annum.

Q6. How much compound interest will be earned on Rs. 24,000 at 16% per annum for 9 months if it is compounded quarterly?

1. 2,887
2. 3,107
3. 3,012
4. 2,997

Answer: 2,997

At 16% per annum compounded quarterly, the rate per quarter is 4%. For 9 months, there are 3 quarters. Amount = \(24000(1.04)^3\approx 26997\), so compound interest = \(26997-24000=2997\).

Q7. A sum of money becomes 2.25 times itself in 2 years at compound interest. What is the rate of interest?

1. 40%
2. 50%
3. 60%
4. 75%

Answer: 50%

If the money becomes 2.25 times in 2 years, then \((1+r)^2 = 2.25\). So \(1+r = 1.5\), giving \(r = 0.5 = 50\%\).

Q8. What will be the amount to be paid at the end of 3 years on Rs. 6000 at 5% per annum compounded annually?

1. 6,845.75
2. 7,045.75
3. 6,945.75
4. 6,955.75

Answer: 6,945.75

For annual compounding, amount after 3 years is \(6000(1.05)^3\). This equals \(6000 \times 1.157625 = 6945.75\). Hence the amount is Rs. 6,945.75.

Q9. A sum of money doubles itself at compound interest in 15 years. In how many years will it become eight times?

1. 45
2. 40
3. 42
4. 35

Answer: 45

If the money doubles in 15 years, then each 15-year period multiplies it by 2. To become eight times, it must double three times because \(8=2^3\). Therefore, the required time is \(3\times15=45\) years.

Q10. A sum of money becomes Rs. 8800 after 2 years and Rs. 9680 after 3 years at compound interest. What is the rate of interest per annum?

1. 8%
2. 10%
3. 12%
4. 15%

Answer: 10%

The amount increases from 8800 to 9680 in one year, so the yearly growth factor is $9680/8800 = 1.1$. This means the rate is 10% per annum.

Q11. Calculate the compound interest on Rs. 5000 for 2 years at 20% per annum, compounded half-yearly.

1. 2,120.50
2. 2,520.50
3. 2,322.50
4. 2,320.50

Answer: 2,320.50

At 20% p.a. compounded half-yearly, the rate per half-year is 10% and the number of periods in 2 years is 4. Amount = 5000(1.1)^4 = 7320.50, so compound interest = 7320.50 - 5000 = 2320.50.

Q12. An amount is said to triple in 6 years with compound interest. How many years will it take for the amount to become 27 times its original value?

1. 18
2. 19
3. 20
4. 21

Answer: 18

If the amount triples in 6 years, then in each 6-year period it is multiplied by 3. Since $27=3^3$, it needs 3 such periods. Therefore, total time = $3\times 6=18$ years.

Q13. A sum becomes ₹7,200 in 2 years and ₹8,640 in 3 years at compound interest. What is the original principal?

1. ₹4,800
2. ₹5,000
3. ₹5,200
4. ₹5,500

Answer: ₹5,000

The ratio of amounts in 3 years and 2 years is $8640/7200=1.2$, so the annual compound factor is 1.2. Therefore, principal $P = 7200/(1.2)^2 = 7200/1.44 = 5000$.

Q14. Find the compound interest on ₹12,000 at 8% per annum for 2 years 9 months, compounded annually.

1. ₹2,456
2. ₹2,598
3. ₹2,712
4. ₹2,837

Answer: ₹2,837

For annual compounding, first calculate the amount after 2 years: \(12000(1.08)^2\). For the remaining 9 months, apply simple interest on this amount for \(\frac{9}{12}\) year at 8%. This gives the compound interest corresponding to the keyed option.

Q15. A sum of Rs 1,25,000 is invested at 12% compound interest per annum. After how many years will it amount to Rs 1,75,616?

1. 2 years
2. 3 years
3. 4 years
4. 5 years

Answer: 3 years

Using \(A=P(1+r/100)^n\), we get \(175616 = 125000(1.12)^n\). Since \(125000 \times 1.12^3 = 175616\), the time is 3 years.

Q16. A person splits Rs 24,000 between two schemes: Scheme A at 18% and Scheme B at 12%, both at simple interest. If the total interest after one year is Rs 3,840, how much was invested in Scheme A?

1. Rs 8,000
2. Rs 10,000
3. Rs 12,000
4. Rs 16,000

Answer: Rs 16,000

Let the amount in Scheme A be \(x\), so Scheme B gets \(24000-x\). The total interest in one year is \(0.18x + 0.12(24000-x)=3840\), which gives \(x=16000\).