ABC bank lends $$200$ million to Company A for a period of $5$ years. The loan is secured by the bank's asset valued at $$60$ million. The following information is available from the credit department of the bank:

Borrower rating of $5$

Probability of default of $1\mathrm{.}35\%$;

Loss given default of $45\%.$

$($i$)$ Calculate the correlation.

$($ii$)$ Calculate the maturity adjustment $($tenor$).$

$($iii$)$ If a minimum capital ratio of $10\%$ is required by the regulator, what is the capital charge for this loan? Give step by step solution