Question

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

Answer 1

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 × $(1+\dfrac{\textrm rate}{2\times 100})^{2\times \textrm time}$

or, 2 P = P  × $(1+\dfrac{\textrm 5}{2\times 100})^{2\times \textrm t}$

Or, 2 = $(1.025)^{2 t}$

Or, Taking log with base 10 both side

So, $Log_{10}$2 = $Log_{10}$ $(1.025)^{2 t}$

or, 0.3010 = 2 t ×  $Log_{10}$ 1.025

Or, 0.3010 =  2 t × 0.010723

Or, 0.3010 = 0.021446 t

∴ t = $\frac{0.3010}{0.021446}$

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