SOLUTION: what interest rate is required for an investment with continuously compounded interest to double in 6 years

Question 219555: what interest rate is required for an investment with continuously compounded interest to double in 6 years
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the continuous compounding interest formula.

Plug in , , and .

Rearrange the terms.

Divide both sides by .

Divide to get .

Take the natural log of both sides.

Pull down the exponent using the identity .

Evaluate to get .

Multiply.

Evaluate to get

Divide both sides by to isolate 'r'

Divide to get

Rearrange the equation.

Round to the nearest ten-thousandth.

So an interest rate of about 11.55% (don't forget to multiply by 100 to convert the decimal to a percent) will make the initial investment of $250 grow to $500 in 6 years.

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