# Math

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How long it will take for an investment of 2000 dollars to double in value if the interest rate is 9.5 percent per year, compounded continuously?

• Math -

Continuously Compounded Interest

Continuously compounded interest is interest that is, hypothetically, computed and added to the balance of an account every instant. This is not actually possible, but continuous compounding is well-defined nevertheless as the upper bound of "regular" compound interest. The formula, is sometimes called the shampoo formula (PertÂ®)

Thus A=Pe ^rt

where e = napier's number or euler's constamt

p = principal/initial investment

r=annual interest rate as a decimal

t = number of years

a = amount of money after t years

thus we plug in to get 4000=2000*e ^9.5t

= 4000 ~= 5436.6^9.5t.

You can solve for t from here

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