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



User Trilby
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Answer:

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

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+(\textrm rate)/(2* 100))^(2* \textrm time)

or, 2 P = P ×
(1+(\textrm 5)/(2* 100))^(2* \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 =
(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

User Nicholas Pesa
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