Question

If you invest $10,000 at 5% interest compounded continuously, what is the average amount in your account over one year?

Answer 1

5% interest compounded continuously. What is meant by continuously? Is that what it says in your question?

Answer 2

yes that is what my question says

Answer 3

Ah I see.

Answer 4

You take the limit of n approaching to infinity.

Answer 5

\[A=Pe ^{rt}\]
\[\int\limits_{}^{}A\ dt=\frac{Pe ^{rt}}{r}+C\]
\[\int\limits_{t=0}^{t=1}A\ dt=\frac{1}{0.05}(10000e ^{0.05}-10000)\]
Can you calculate the average value now?

Answer 6

yes thank you

Answer 7

Cool!