In what time will a sum of money double itself at 5 parcent compound interest payable half yearly

The Time in which sum of money double itself is 14 years .

Step-by-step explanation:

Given as :

The principal money = P

The rate of interest = R = 5 %  payable half yearly

The Amount = Double of principal

Let The time in which sum become double = t years

I.e A = 2 P

From Compounded method

Amount = principal ×

or, 2 P = P  ×

Or, 2 =

Or, Taking log with base 10 both side

So, 2 =

or, 0.3010 = 2 t ×   1.025

Or, 0.3010 =  2 t × 0.010723

Or, 0.3010 = 0.021446 t

∴ t =

I.e t = 14.03 years ≈ 14 years

So, The time period = T = 14 years

Hence The Time in which sum of money double itself is 14 years . Answer