lim _{n rightarrow infty} Pleft(1+frac{r}{100 | vedclass

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Question

(C) Let $y = \lim _{n \rightarrow \infty} P\left(1+\frac{r}{100 n}\right)^{t n}$.We know the standard limit formula $\lim _{k \rightarrow \infty} (1+\

Vedclass · Accepted Answer

$P e^{\frac{r t}{100}}$

Vedclass · Answer

(C) Let $y = \lim _{n \rightarrow \infty} P\left(1+\frac{r}{100 n}\right)^{t n}$.We know the standard limit formula $\lim _{k \rightarrow \infty} (1+\frac{x}{k})^k = e^x$.Here,let $k = n$. Then the expression becomes $P \left[ \lim _{n \rightarrow \infty} (1+\frac{r/100}{n})^n \right]^t$.Using the limit formula,$\lim _{n \rightarrow \infty} (1+\frac{r/100}{n})^n = e^{r/100}$.Therefore,$y = P \left( e^{r/100} \right)^t = P e^{\frac{rt}{100}}$.

$\lim _{n \rightarrow \infty} P\left(1+\frac{r}{100 n}\right)^{t n} =$

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