Question

Suppose a person deposits ₹ 10,000 in a bank account at the rate of 5% per annum compounded continuously. How much money will be in his bank account 18 months later?

Answer 1

Let P be the principal amount

Given Rate of interest = 5% per annum.

∴ `"dP"/"dt" = "P"(5/100)` = 0.005P

The equation can be written as,

`"dP"/"P"` = 0.05 dt

Taking Integration on both sides, we get

`int "dP"/"P" = 0.051 int "dt"`

log P = 0.05 t + log c

log P – log C = 0.05t

`log ("P"/"C")` = 0.05t

`"P"/"C"` = e^0.05t

P = `"Ce"^(0.05"t")`  .........(1)

Initial condition:

Given when t = 0; P = 10,000

Substituting these values in equation (1), we get

P = `"Ce"^(0.05"t")`

10,000 = `"Ce"^(0.05 (0))`

10,000 = C e°

C = 10,000

∴ Substituting the C value in equation (1), we get

P = 10,000 e^0.05t  .........(2)

When t = 18 months

= `1 1/2` yr

= `3/2` years, we get

(2) ⇒ P = `10,000 "e"^(0.05 (3/2))`

P = 10,000 e^0.075

The amount in a bank account be

P = 10,000 e^0.075