Find the compound interest on ₹ 15625 for 9 months at 16% per annum compounded quarterly.

### Concept & Quarterly Compounding For quarterly compounding, divide the annual interest rate by 4 and multiply the number of years by 4 to get the total number of compounding periods (quarters). $$ A = P(1 + \frac{R/4}{100})^{4n} $$ ### Step-by-Step Solution * **Given:** Principal ($P$) = ₹ 15625, Rate = 16% p.a., Time = 9 months. * **Step 1:** Adjust the rate and time for quarterly cycles. Quarterly Rate = $\frac{16\%}{4} = 4\%$ per quarter. Time Periods = 9 months = 3 quarters. * **Step 2:** Formulate the compound interest equation. $A = 15625 \times (1 + \frac{4}{100})^3$ $A = 15625 \times (\frac{26}{25})^3$ * **Step 3:** Calculate the powers. Note that $25^3 = 25 \times 25 \times 25 = 15625$. $A = 15625 \times \frac{17576}{15625}$ * **Step 4:** Cancel the common terms and find the interest. $A = 17576$ $CI = A - P = 17576 - 15625 = 1951$ ### Exam Strategy & Shortcut Memorize common cubes like $25^3 = 15625$ and $26^3 = 17576$. When you see 15625 in a problem with a 4% rate (which fractionally is $\frac{1}{25}$ leading to a multiplier of $\frac{26}{25}$), you can instantly deduce the final amount will be $26^3$ if the time is 3 cycles. $17576 - 15625 = 1951$. ### Common Pitfall Forgetting to convert 9 months into 3 distinct quarters, or multiplying the rate instead of dividing it. ### Final Answer Therefore, the correct answer is **₹ 1951**.