If an initial amount A 0 of money is invested at aninterest rate r compounded n times a year, the value of the investment after t years is: A = A 0 ( 1 + r n ) ◻ n t If we let n → ∞ we refer to the continuous compounding of interest. Use L'Hospital's Rule to show that if interest is compounded continuously, then the amount aftert years is A 0 e r t

Question

If an initial amount       A          0       of money is invested at aninterest rate r compounded n times a year, the value of the investment after t years is:  A  =      A          0        (  1  +      r    n    )      ◻          n      t      If we let   n  →  ∞ we refer to the continuous compounding of interest. Use L&#039;Hospital&#039;s Rule to show that if interest is compounded continuously, then the amount aftert years is      A          0            e          r      t

Bianca Chung · Accepted Answer

Given that If an initial amount       A          0       of money isinvested at an interest rate r compounded n times a year, the value of the investment after t years iswe know that as   n  →  ∞  (  1  +      r    n        )          n        =      e          r      Therefore   A  =      A          0            e          r      t