$-2\mathrm{.}1\mathrm{.}31$ Smith borrows $5000$ on January $1,2015.$ She repays the loan with

$20$ annual payments starting January $1,2016.$ The payments in

even$-$numbered years are $Y$ each and the payments in odd$-$num$-$

bered ycars are $x$ each. If $i=\mathrm{.}08$ and the total of all $20$ loun pay$-$

ments is $10,233,$ find $x$ and $Y.$

$"2\mathrm{.}1\mathrm{.}32$ A loan of $11,000$ is made with interes: at a nominal annual rate of

$12\%$ compounded monthly. The loan is to be repaid by $36$ monthly

payments of $367\mathrm{.}21$ over $37$ months, starting one month after the

loan is made, there being a payment at the end of every month but

one. At the end of which month is the missing payment?