Q. 95.0( 1 Vote )

# A ban pays interest by continuous compounding, that is, by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accrues at 8% per year, compounded continuously. Calculate the percentage increase in such an account over one year.[Take e0.08≈1.0833]

Let the principal, rate and time be Rs P, r and t years.

Also, let the initial principal be Po.

Integrating both sides, we have

∫dt

log|P| = t + c……(1)

Now, at t = 0, P = Po

log| Po | = 0 + c

c = log| Po |……(2)

Putting the value of c in equation (1) we have,

log|P| = t + log|Po|

log|P| – log|Po| = t

(log |P| – log|Po|) = t []

log ( = t ……(3)

Now, t = 1 year, r = 8%

log ( = ×1

log ( = 0.08

(Given: = 1.0833)

Percentage increase = 0.0833×100 = 8.33%

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