What would be the compound interest accrued on an amount of ₹ 8000 at the rate of 15 p.c.p.a. in 3 years?

### Concept & Compound Interest The compound interest is found by first calculating the total amount accumulated over the time period, then subtracting the principal. $$ A = P(1 + \frac{R}{100})^n $$ $$ CI = A - P $$ ### Step-by-Step Solution * **Given:** Principal ($P$) = ₹ 8000, Rate ($R$) = 15% p.a., Time ($n$) = 3 years. * **Step 1:** Apply the compound interest formula to find the Amount ($A$). $A = 8000 \times (1 + \frac{15}{100})^3$ $A = 8000 \times (1 + \frac{3}{20})^3$ $A = 8000 \times (\frac{23}{20})^3$ * **Step 2:** Expand and calculate. $A = 8000 \times \frac{12167}{8000}$ * **Step 3:** The 8000 in the numerator and denominator cancel out. $A = 12167$ * **Step 4:** Calculate the Compound Interest. $CI = A - P = 12167 - 8000 = 4167$ ### Exam Strategy & Shortcut Instead of heavy multiplication, use successive percentages or the 3-year multiplier rule ($3r : 3r^2 : r^3$). Alternatively, realize that $15\% = \frac{3}{20}$. The amount scales by $\frac{23}{20}$ each year. Since the principal is exactly $20^3$ (which is 8000), the final amount is exactly $23^3 = 12167$. Subtract 8000 to get 4167 instantly. ### Common Pitfall Calculating $15\%$ of 8000 and just multiplying by 3 (Simple Interest). This gives 3600, which is incorrect for compound interest. ### Final Answer Therefore, the correct answer is **₹ 4167**.