Q81 / 150 · MHT CET 2025 (20 Apr Shift 1) · Mathematics

The money invested in a company is compounded continuously. ₹400 invested today becomes $₹ 800$ in 6 years, then at the end of 33 years, it will become $_{-}(\sqrt{2} = 1 \cdot 4142)$

  • A
    $9050 \cdot 88$
  • Correct answer
    B
    $18101 \cdot 76$
  • C
    $6788 \cdot 16$
  • D
    $12067 \cdot 84$

Solution

Continuous compounding follows the formula $A = Pe^{rt}$, where $P$ is the principal, $r$ the annual rate, and $t$ the time in years.

To find $r$, set $P = 400$, $A = 800$, and $t = 6$:
$800 = 400e^{6r}$
$2 = e^{6r}$
Taking natural logarithms: $\ln(2) = 6r$, so $r = \frac{\ln(2)}{6}$.

For $t = 33$ years, with the same $P$ and $r$:
$A = 400e^{\left(\frac{\ln(2)}{6}\right) \cdot 33} = 400e^{5.5\ln(2)} = 400e^{\ln(2^{5.5})} = 400 \cdot 2^{5.5}$

Since $2^{5.5} = 2^5 \cdot 2^{0.5} = 32\sqrt{2} \approx 32 \cdot 1.4142 = 45.2544$,
$A = 400 \cdot 45.2544 = 18101.76$

This matches option B.

Hence, the correct answer is option: 'B'.

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