Question

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 (e^0.5 = 1.648).

Answer 1

At some time t, the principal is P then according to the question,

`(dP)/dt = (5/100) xx P`

`(dP)/P = 5/100   dt`

`=> (dP)/P = 1/20  dt`

On integrating

log P `= 1/20` . t + C₁

P = e^t/20 + C₁ = e^C₁ e^t/20

`P = C  e^(t/20)`   (where e^C₁=C)            .... (i)

When P = 1000, t = 0 then

1000 = Ce⁰

⇒ 1000

From equation (i)

`P = 1000   e^(t/20)`

When t = 10 years

`p = 1000  e^(10/20)`

⇒ P = 1000 e^0.5

P = 1000 × 1.648 (∵ e^0.5 = 1.648)

⇒  P = 1648 Rs.

Hence, the principal after 10 years will be Rs 1648.