# Thread: limits and compound interest

1. ## limits and compound interest

Given the compund interest equation A= P(1+r/100n)^n. find the final amount if the intial deposit is $1500, the rate is 7% and the time period , n, approaches infinity 2. Originally Posted by math123456 Given the compund interest equation A= P(1+r/100n)^n. find the final amount if the intial deposit is$1500, the rate is 7% and the time period , n, approaches infinity
Here, all you need to do is evaluate $\displaystyle \lim_{n\to\infty}1500\left(1+\frac{r}{100n}\right) ^n$

Take note that this resembles the limit definition for $\displaystyle e$: $\displaystyle \lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n=e$ and in general $\displaystyle \lim_{n\to\infty}\left(1+\frac{a}{n}\right)^n=e^a$ (I leave it for you to show this is the case. You will need to apply L'Hopitals rule to this).

Thus, $\displaystyle A=\lim_{n\to\infty}1500\left(1+\frac{r}{100n}\righ t)^n=1500\lim_{n\to\infty}\left(1+\frac{\frac{r}{1 00}}{n}\right)^n=1500e^{\frac{r}{100}}$. Since $\displaystyle r=.07$, we have $\displaystyle A=1500e^{\frac{0.07}{100}}\approx 1501.05$

Does this make sense?