The balance $B$ of a savings account after $t$ years when a principal $P$ is invested at an annual interest rate $r$ and the interest is compounded $n$ times a year is given by:

$B=P(1+\frac{r}{n}{)}^{nt}$

$(1)$

If the interest is compounded yearly, the balance is given by:

$B=P(1-r{)}^t$

Suppose $$5,000$ is invested for $17$ years in one account for which the interest is compounded yearly. In addition, $$5,000$ is invested in a second account in which the interest is compounded monthly. In both accounts the interest rate is $8\mathrm{.}5\%.$ Use MATLAB to determine how long $($in years and months$)$ it would take for the balance in the second account to be the same as the balance of the first account after $17$ years.