You observe that the current interest rates for $1-$year T$-$strips and $1-$year corporate strips are $2\mathrm{.}4\%$ and $6\mathrm{.}5\%,$ respectively. The rates for their corresponding $2-$year strips are $3\mathrm{.}2\%$ and $9\mathrm{.}8\%,$ respectively. As a bank loan officer, you estimate that you can recover $60\%$ from collateral of a loan in the event of default. What is the default probability of the loan in the first year?

A$.9\mathrm{.}62\%$