Consider the compound interest of the following

(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is: Rs 2522
(B) The compound interest on Rs 2800 at 10% per annum for 18 months, compounded annually is: Rs 434

Choose the correct statement(s):

Both (A) and (B)

The correct answer is Option (3) → Both (A) and (B)

Verification of Statement (A):

• Principal ($P$): Rs 16,000
• Rate ($R$): 20% per annum $\rightarrow$ Since it is compounded quarterly, the rate per quarter is $20\% / 4 = 5\%$.
• Time ($n$): 9 months $\rightarrow$ There are $9/3 = 3$ quarters in 9 months.
• Formula: $A = P \times (1 + \frac{r}{100})^n$

$A = 16000 \times (1 + \frac{5}{100})^3$

$A = 16000 \times (1.05)^3$

$A = 16000 \times 1.157625 = 18522$

• Compound Interest ($CI$): $A - P = 18522 - 16000 = \text{Rs } 2522$.
• Conclusion: Statement (A) is correct.

Verification of Statement (B):

• Principal ($P$): Rs 2,800
• Rate ($R$): 10% per annum
• Time: 18 months (1.5 years)
• Compounding: Annually. For fractional years with annual compounding, we calculate for the full year and then apply simple interest to the amount for the remaining period.
• Interest for Year 1: $2800 \times 10\% = 280$. Amount = $2800 + 280 = 3080$.
• Interest for the next 6 months (0.5 year): $3080 \times 10\% \times 0.5 = 154$.
• Total Interest: $280 + 154 = \text{Rs } 434$.
• Conclusion: Statement (B) is correct.

Final Answer:

Since both calculations match the values given in the prompt, the correct option is Both (A) and (B).