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Question -

In a bank, principal increases continuouslyat the rate of r% per year. Find the value of r ifRs 100 doubles itself in 10 years (log­e 2 = 0.6931).



Answer -

Let pt, and r representthe principal, time, and rate of interest respectively.

It is given that the principal increasescontinuously at the rate of r% per year.

Integratingboth sides, we get:

It is given that when t =0, p = 100.

100 = ek … (2)

Now, if t = 10, then p =2 × 100 = 200.

Therefore,equation (1) becomes:

Hence,the value of r is 6.93%.

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