If an initial amount A(0) of money is in...

If an initial amount `A_(0)` of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is `A=A_(0)(1+1/n)^(nt)`. If the interest is compounded continuously, (that is as `ntooo`), show that the amount after t years is `A=A_(0)e^(rt)`.

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If an initial amount `A_(0)` of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is `A=A_(0)(1+1/n)^(nt)`. If the interest is compounded continuously, (that is as `ntooo`), show that the amount after t years is `A=A_(0)e^(rt)`.

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