Question

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 .. (√2 = 1.4142)

Options

• 9050.88

• 18101.76

• 6788.16

• 12067.84

Answer 1

18101.76

Explanation:

Here, Amount (A) = ₹ 800

Principal (P) = ₹400, N = 6 years

\[\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^\mathrm{N}\]

\[\therefore\quad800=400\left(1+\frac{\mathrm{R}}{100}\right)^6\]

\[\therefore\quad1+\frac{\mathrm{R}}{100}=2^{\frac{1}{6}}\]

\[\mathbf{A}=\mathbf{P}\left(1+\frac{\mathbf{R}}{100}\right)^{\mathbf{N}}\]

\[=200\left(1+\frac{\mathrm{R}}{100}\right)^{33}\]

\[=200\left(1+\frac{\mathrm{R}}{100}\right)^{33}\]

\[=200\left(2^{\frac{1}{6}}\right)^3\]

\[=200\left(2^52^{\frac{1}{2}}\right)\]

\[=200\times32\times\sqrt{2}\]

= ₹ 18101.76