In a bank, the principal increases continuously at a rate of x % per year. Then the rate, x , if ₹100 double itself in 10 years, is ( 2=0.6931)

Step-by-step solution

The principal grows continuously at x % per year, following the continuous compounding formula A = Pe^ rt . Given P = ₹ 100 , A = 2P = ₹ 200 , and t = 10 years, with r = x 100 . Substituting into the formula yields 200 = 100e^ ( x 100 ) 10 , which simplifies to 2 = e^ x 10 . Taking natural logarithms gives 2 = x 10 . Using 2 = 0.6931 , we find x = 10 0.6931 = 6.931 . The rate is approximately 6.93 % , matching option A .