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

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asked Oct 25, 2018

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

## 1 Answer

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answered Oct 28, 2018 by (460 points)

Hi!

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

Also your workings to get to the final probability seem correct as well.

In terms of showing enough detail in your workings: everything seems to be up to scratch. If you want to double check, though, I would recommend going to see Dr Sure. He has the final say in terms of the level of detail that is required for each question.