Question

In how many years a sum of 2000 becomes 2205 at the rate of 5% p.a.compound interest

Answer 1

given :

principal :

=> 2,000 rs

amount :

=> 2,205 rs

rate of interest :

=> 5%

____________________________


amount - principal

=> 2,205 - 2,000

=> 205 rs

___________________________


amount = p ( 1 + r / 100 ) ^ n

=> 2205 = 2000 ( 1 + 5 / 100 ) ^ n

=> 2205 / 2000 = ( 1 + 5 / 100 ) ^ n

=> 441 / 400 = ( 1 + 5 / 100 ) ^ n

=> 441 / 400 = ( 105 / 100 ) ^ n

=> 441 / 400 = ( 21 / 20 ) ^ n

=> but ,

=> 21^ 2 = 441

=> 20^2 = 400

=> so,

=> 441 / 400 = ( 21 / 20 ) ^ 2

=> n = 2

____________________________


so ,

=> the time period :

=> 2 yrs

Answer 2

$\huge\bold{Solution\:here}$

Principal => 2,000 RS

Amount =>2,205

Rate of interest => 5%

Amount - Principal

=>2,205 - 2,000

=> 205 RS

Amount = $\p \:{ \:1\:+r\:/ \:100\:} ^{2}$

=> 2205 = 2000 ${1+5/100}^{n}$

=>2205/ 2000 = ${1+5+/100}^{n}$

=>441/400 =${1+5/100}^{n}$

=>441/400 =${105/100}^{n}$

=>441/400 =${21/20}^{n}$

=>21^ 2 = 441.

=>20^2= 400.

=>441/400 = (21/20)^2.

N = 2..