As a result of the credit crunch, a small retail bank wants to better predict and model the likelihood that its larger commercial loans might default. It is developing an internal ratings-based approach to assess its commercial customers. Given this one-year transition matrix, what is the probability that a loan currently rated at B will default over a two-year period?

| Rating at Beginning of Period | Rating at End of Period | | | |

|------------------------------|-------------------------|-------|-------|-------|

| | A | B | C | D |

| A | 0.90 | 0.10 | 0.00 | 0.00 |

| B | 0.00 | 0.75 | 0.15 | 0.10 |

| C | 0.00 | 0.05 | 0.55 | 0.40 |