Q. 554.3( 3 Votes )

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

Answer :

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 = ek .....--(2)


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


=


= from (2)


=


=


=


= r = 6.931


Hence, the value of r is 6.93 %.


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