I know I am not using the precise termonoly for a repo as it sale and repurchase and not a loan.
With the colateral on the implict loan in the contract we are consantly having to mark to market as the underlyng security chnages in value.
Initally.
We sell a bond with par 100m
Put the buyer wants security so won’t lend us 100m
The will only lend 100/1.02 = 98.039216
Think of this another way the value of the colateral/bond the lender has has got to 102% of the value of the loan.
Loan = 98.039216m
Colaterial 98.038216 x 1.02 = 100m
5 days pass. Interest accumlates on the loan.
Borrower now owes 98.042620 (we have just increased the value by 0.25% over 5 days.
So the colaterial required is 98.04262 x 1.02 = 100.034722
The bond uses as colateral though has a market value of 103 (more than required)
The borrower can then request back some of the bond
Price value of amount that can be retuned = 103 - 100.034722 = 2.996528
The asummption here than is the bond was selling at par at start of loan (I assume that is in previous part of question) and is now selling 1.03x par (103/100 = 1.03)
So par value to be returned = 2.996528 / 1.03 = 2.91