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)

Step-by-step 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: (2) = 6r , so r = (2) 6 . For t = 33 years, with the same P and r : A = 400e^ ( (2) 6 ) 33 = 400e^ 5.5 (2) = 400e^ (2^ 5.5 ) = 400 2^ 5.5 Since 2^ 5.5 = 2^5 2^ 0.5 = 32 2 32 1.4142 = 45.2544 , A = 400 45.2544 = 18101.76 This matches option B .