The money invested in a company is compounded continuously. If Rs. 400 invested today becomes Rs. 800 in 6 years, then at the end of 30 years, it will become (in Rs.) ______.
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Shortcut for Doubling Time: If money doubles every 6 years, then in 30 years it will undergo $30 / 6 = 5$ complete doubling cycles.
$400 \times (2)^5 = 400 \times 32 = 12800$. No $e$ or $\ln$ is required!
Step 1: Understanding the Concept:
Continuous compounding follows the formula $A = Pe^{rt}$. If the amount doubles in a fixed time $T$, it will continue to double every $T$ years (geometric growth). Step 2: Formula Application:
Initial Principal ($P$) = 400.
After 6 years ($T=6$), $A = 800$ (Double). Step 3: Explanation:
The investment doubles every 6 years.
In 30 years, the number of "doubling periods" is $30/6 = 5$.
Amount after 30 years = $P \times 2^5 = 400 \times 32 = 12800$. Step 4: Final Answer:
The amount will become ₹12800.