How long will it take to double an investment with the interest computed daily at 12%, 365days/year?

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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You need to use the formula for compound interest which is

A is the future value - ie. double and therefore A = 2P

P is the current value of the investment.

r (sometimes expressed as i) is the rate of interest. Note that it is divided by 100 as a percentage is any amount out of 100.

n is the number of years 

Care to adjust the formula to allow for the daily compounding by dividing by 365.

If it is compounded annually you divide by 12 and so on. Also multiply by 365 - the same number as you divided by.

You are ready to put all this info into the formula:

`2P = P(1+(r/100)/365)^(n times 365)`

`(2P)/P= 1.1000328767^(365n)`

Care not to round off too soon. The `(2P)/P` cancels out the P:

`therefore 2= 1.000328767^(365n)`

As the unknown (n) is part of the exponent use the laws of logs to solve

`therefore log 2 = log 1.000328767^(365n)`

`log 2= 365n log 1.000328767`

`(log 2)/(log 1.000328767)= 365n`

`2108.670019/365 = n`

You will be able to plug these values into your calculator without finding individual balances each time to ensure an accurate answer

`therefore n= 5.78` years.

Rounded off to the nearest year  equals 6 years.  

Sources:

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