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Math Help - limits and compound interest

  1. #1
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    Exclamation 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
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by math123456 View Post
    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 \lim_{n\to\infty}1500\left(1+\frac{r}{100n}\right)  ^n

    Take note that this resembles the limit definition for e: \lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n=e and in general \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, 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 r=.07, we have A=1500e^{\frac{0.07}{100}}\approx 1501.05

    Does this make sense?
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