Use the following information for the next $5$ questions

A four$-$year fixed$-$rate loan of $$50$ million carries a $5\mathrm{.}5$ percent annual interest rate. The borrower is rated Baa. Based on hypothetical historical data, the probability distribution given below has been determined for various ratings upgrades, downgrades, status quo, and default possibilities over the next year. Information also is presented reflecting the forward rates of the current Treasury yield curve and the annual credit spreads of the various maturities of A bonds over Treasuries.

$\backslash$table$[[$Rating$,$New Loan.,,,$],[$Probability$,$Value pls$,,,$Forward,Rate Spreads at Time t$],[$Distribution$,$Coupon,,$t,,t(\%).],[$Aaa$,0\mathrm{.}72\%,$$$52\mathrm{.}82m,1,,5\mathrm{.}10\%,0\mathrm{.}98\%$

The next questions are:

$1.$ What is the present value of the loan at the end of the one$-$year risk horizon for the case where the borrower has been upgraded from Baa to A$?$

$2.$ What Is the mean value of thw loan at the end of year $1?$

$3.$ What is the volatility of the loan value at thw end of year $1?$