Question

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

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Answer 1

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