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

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### 1 Answer

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. **

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