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Contingent Immunization -- change in YTM
Can you help me please with something I just don't understand (or forgot perhaps) on page 37 of Volume 4 of the CFAI textbooks (Reading 20). There is a bit about contingent immunisation on page 36 and they discuss it with the example of a $500 million portfolio (at the beginning).
On page 37:
'If the manager invests the entire $500 million in a 4.75%, 10 year notes at par and the YTM immediately changes, what will happen to the dollar safety margin?
If the YTM suddenly drops to 3.75%, the value of the portfolio will be $541.36…'
Can you guide me how to get this calculation? I don't remember all the stuff about the bond yields and YTM etc, so I'm puzzled about how they got this value from a YTM of 3.75%.