In a bank principal increases at the rate of r% per year. Find the value of r if ` 100 double itself in 10 years (log_e 2 = 0.6931).

Let p, t, and r represent the principal, time and rate of interest respectively.

It is the given that the principal increases continuously at the rate r% per year.

Find: Find the value of r?

=

=

Integrating both sides, we get:

=

=

= p = .....-(i)

It is given that when t = 0, p = 100

= 100 = e^k .....--(2)

Now, if t =10,then p = 2x100 =200

=

= from (2)

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=

=

= r = 6.931

Hence, the value of r is 6.93 %.