In a bank, principal increases continuously at the rate of 5% per yea…

let p and t  be the principal and time respectively.

It is given that the principal increases continuously at the rate 5% per year.

⇒(dp/dt) = (5/100)p

⇒dp/p = dt/20

Integrating both sides, we get:

p = e^{(t/20 +C)} ....................(i)

when, t = 0, p=1000

⇒1000= e^C........................(ii)

at t = 0, equation (i) becomes:

p = e(^{1/2 + C)}

⇒p = 1648

Hence, after 10 years the amount will worth Rs. 1648.