In a bank the principal increases continuously at the rate of 4% per annum. In how many years will ₹1000 triple itself?

Step-by-step solution

Let P be the principal at any time t . The rate of increase of principal is given by dP dt = 4 100 P dP P = 0.04 dt Integrating both sides: dP P = 0.04 dt _e P = 0.04 t + C At t = 0 , P = 1000 , which gives C = _e 1000 Substituting C back into the equation: _e P = 0.04 t + _e 1000 _e ( P 1000 ) = 0.04 t To find the time when the principal triples, substitute P = 3000 : _e ( 3000 1000 ) = 0.04 t _e 3 = 4 100 t t = 25 _e 3 Answer: 25 _e 3