A man gets a simple interest of ₹ 1000 on a certain principal at the rate of 5 p.c.p.a. in 4 years. What compound interest will the man get on twice the principal in 2 years at the same rate?

### Concept & Simple to Compound Transition First, use the Simple Interest (SI) formula to isolate and find the unknown original principal. Then, apply the Compound Interest (CI) formula on the new manipulated principal. $$ SI = \frac{P \times R \times T}{100} $$ ### Step-by-Step Solution * **Given (Part 1):** SI = ₹ 1000, Rate = 5% p.a., Time = 4 years. * **Step 1:** Find the original Principal ($P$). $1000 = \frac{P \times 5 \times 4}{100}$ $1000 = \frac{20P}{100}$ $P = \frac{1000 \times 100}{20} = 5000$ * **Given (Part 2):** New Principal = Twice the original = $2 \times 5000 = 10000$. Rate = 5% p.a., Time = 2 years. * **Step 2:** Calculate the Compound Amount ($A$) for the new principal. $A = 10000 \times (1 + \frac{5}{100})^2$ $A = 10000 \times (1.05)^2$ $A = 10000 \times 1.1025 = 11025$ * **Step 3:** Calculate the new Compound Interest. $CI = A - \text{New Principal} = 11025 - 10000 = 1025$ * **Step 4:** Compare the result with the given options. ₹ 1025 is not listed among options (a), (b), (c), or (d). ### Exam Strategy & Shortcut You can do this mentally: 5% for 4 years is 20% total interest. If 20% of P is 1000, then 100% of P is 5000. Twice the principal is 10000. 5% CI for 2 years has an effective rate of $5 + 5 + 0.25 = 10.25\%$. Find 10.25% of 10000, which is exactly 1025. ### Common Pitfall Misreading "twice the principal" and calculating CI on the original 5000 (which gives 512.5), or confusing the calculated Amount (11025, option d) as the Interest. ### Final Answer Therefore, the correct answer is **None of these**.