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).
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 %.