amacorrit80

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:
$A={A}_{0}\left(1+\frac{r}{n}\right){◻}^{nt}$
If we let $n\to \mathrm{\infty }$ 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
${A}_{0}{e}^{rt}$

Bianca Chung

Expert

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 $n\to \mathrm{\infty }\left(1+\frac{r}{n}{\right)}^{n}={e}^{r}$
Therefore $A={A}_{0}{e}^{rt}$

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