Practicing Success
In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs. 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 =1.648) |
1648 1748 1848 1668 |
1648 |
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= eC........................(ii) at t = 0, equation (i) becomes: p = e(1/2 + C) ⇒p = 1648 Hence, after 10 years the amount will worth Rs. 1648.
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