Question

In a bank, principal increases 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)`

Options

• 1648

• 1300

• 896

• 2249

Answer 1

1648

Explanation:

Let P be the principal rate of interest is 5%

∴ `(dp)/(dt) = 5/100` P

∴ `(dp)/p = 0.05  dt`

Integrating, we get, log p = 0.05 t + log c

or `p/c = e^(0 - 0.5 t)`

∴ `p = ce^(0.05 t)`  .......(1)

Putting p = Rs 1000, t = 0

1000 = `ce^0` = c ⇒ c = 1000

Putting this value in (1),

P = `1000  e^(0.05t) d`

When t = 10, p = `1000  e^(0.05 xx 10) = 1000  e^(0.5)`

P = `1000 xx 1.648`

∴`e^(0.5)` = 1648