Answer:
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 × [tex](1+\dfrac{\textrm rate}{2\times 100})^{2\times \textrm time}[/tex]
or, 2 P = P × [tex](1+\dfrac{\textrm 5}{2\times 100})^{2\times \textrm t}[/tex]
Or, 2 = [tex](1.025)^{2 t}[/tex]
Or, Taking log with base 10 both side
So, [tex]Log_{10}[/tex]2 = [tex]Log_{10}[/tex] [tex](1.025)^{2 t}[/tex]
or, 0.3010 = 2 t × [tex]Log_{10}[/tex] 1.025
Or, 0.3010 = 2 t × 0.010723
Or, 0.3010 = 0.021446 t
∴ t = [tex]\frac{0.3010}{0.021446}[/tex]
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
