# How to do Stochastic Interest rate problems with lognormally distributed accumulation factors (practice question)

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Hi

I've attached a question from the 2015 exam on stochastic interest rates, and an attempt at an answer.

I have two questions:

1.) Is this attempt correct, if not, where did it go wrong?

2.) when we do this type of question do we have to show most of the deriving of distributions etc. (as done here) or is it fine to just the use the formulas for this case that were derived in lectures?

Thanks

P.S excuse the bad picture quality

I have gone through everything. Your value for $$\sigma^2$$ is correct (I assumed that your value for $$\mu$$ was correct thereafter).