In a bank, the principal increases continuously at the rate of r% per year. Find the value of r if Rs. 100 double itself in 10 years (Take log_e2 = 0.6931).

Let the Principle be p

Since, it is given principle is increasing continuously at a rate of r% per year

Therefore,

Integrating both sides

Since,

Taking anti - log both side

…(i)

Since, Time = 0 , then principal = 100

If , Time = 10 , then principal = 200 (Double ) Given

So, putting t = 0 and p = 100 in equation (i)

C = 100

Now, Put the value of C in equation (i), we get

….(ii)

And, After 10 years , the principal is double

Then, Put t = 10 and p = 200 in equation (ii)

Taking log both side, we get

Since, log 2 = 0.6931 (Given)

r = 6.931

Hence, The rate of interest is 6.931%