If an initial amount A_0 of money is invested at aninterest rate r compounded n times a year, the value of theinvestment after t years is: A=A_0 (1+r/n)square^(nt) if we let n rightarrow infty we refer to the continuous compounding of interest. Use L'Hospital's Rule to showthat if interest is compounded continuously, then the amount aftert years is A = A_0 e^(rt)

amacorrit80

amacorrit80

Answered question

2022-07-24

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

Answer & Explanation

Bianca Chung

Bianca Chung

Beginner2022-07-25Added 16 answers

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 is
we know that as n ( 1 + r n ) n = e r
Therefore A = A 0 e r t

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