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Question $1$

The following is the cumulative average default rates collected by Moody's. What is the probability that a bond initially rated Ba defa

$\backslash$table$[[$Time $($years$),1,2,3,4,5,7,10],[$Aaa$,0\mathrm{.}000,0\mathrm{.}013,0\mathrm{.}013,0\mathrm{.}037,0\mathrm{.}104,0\mathrm{.}241,0\mathrm{.}489],[$Aa$,0\mathrm{.}022,0\mathrm{.}068,0\mathrm{.}136,0\mathrm{.}260,0\mathrm{.}410,0\mathrm{.}682,1\mathrm{.}017],[$A$,0\mathrm{.}062,0\mathrm{.}199,0\mathrm{.}434,0\mathrm{.}679,0\mathrm{.}958,1\mathrm{.}615,2\mathrm{.}759],[$Baa$,0\mathrm{.}174,0\mathrm{.}504,0\mathrm{.}906,1\mathrm{.}373,1\mathrm{.}862,2\mathrm{.}872,4\mathrm{.}623],[$Ba$,1\mathrm{.}110,3\mathrm{.}071,5\mathrm{.}371,7\mathrm{.}839,10\mathrm{.}065,13\mathrm{.}911,19\mathrm{.}323],[$B$,3\mathrm{.}904,9\mathrm{.}274,14\mathrm{.}723,19\mathrm{.}509,23\mathrm{.}869,31\mathrm{.}774,40\mathrm{.}560],[$Caa$,15\mathrm{.}894,27\mathrm{.}003,35\mathrm{.}800,42\mathrm{.}796,48\mathrm{.}828,56\mathrm{.}878,66\mathrm{.}212]]$

$5\mathrm{.}371\%$

$9\mathrm{.}552\%$

$1\mathrm{.}961\%$

$2\mathrm{.}300\%$