Chapter 1, Problem 21RE

If $\text{\$}1000$ is invested in an account that pays $7\%$ interest compounded $n$ times each year, then in $10$ years there will be $1000{\left(1+0.07/n\right)}^{10n}$ dollars in the account. How much money will be in the account in $10$ years if the interest is compounded quarterly $\left(n=4\right)$ ? Monthly $\left(n=12\right)$ ? Daily $\left(n=365\right)$ ? Determine the amount of money that will be in the account in $10$ years if the interest is compounded continuously, that is, as $n\to +\infty$ .