Contingent Immunization — change in YTM

Question

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%.

vincentt · Answer

"...he manager invests the entire $500 million in a 4.75%, 10 year notes at par."

PV=-500
N=20
I/Y=4.75 / 2 
PMT= 500 * 0.0475 / 2 (since it's par)
FV = 500

or leave PV off and so CPT -> PV, you'll get -500 anyway.

now key in I/Y = 3.75 / 2
then CPT -> PV

You should get 541.37

MockTurtle · Answer

Got it, thanks @vincentt! I was entering the data wrong in my calculator, so got quite puzzled!