$2.$ Bond dealers often finance their positions through the repo market. Since repos are very short$-$term $($usually no more than a few days$)$ collateralized loans, the interest paid on the repo is usually less than the interest earned on the bond that is being carried $($when the yield curve is upward sloping$).$ This allows the bond dealer to earn profits on $(1)$ the spread, $(2)$ any appreciation of the bond while it is owned, and $(3)$ the carry. Note though, that there is risk to holding a bond.

Here is price data for a $4(1)/(2)\%$ Treasury bond with a maturity date of May $15,2030,$ along with the repo rates, for a week in October $2023.$

Posted Treasury Quotes Overnight Repo Rates

Date Bid Ask APR

$10/9/23101$:$18101$:$204\mathrm{.}30\%$

$10/10/23101$:$19101$:$214\mathrm{.}34$

$10/11/23101$:$21101$:$234\mathrm{.}36$

$10/12/23101$:$24101$:$264\mathrm{.}40$

$10/13/23101$:$23101$:$254\mathrm{.}43$

Assume that on Monday October $9,$ an insurance company contacted you, a bond dealer, and sold you $$100$ million $($face value$)$ of the $4(1)/(2)\%5/15/30$ T$-$Bond at your quoted price. You carried the position in the repo market $($one day at a time$)$ for four days at a haircut of $0\mathrm{.}5\%$ before being contacted Friday morning $($Oct$.13)$ by a pension plan that purchased the bond from you at your quoted price. For simplicity, assume that settlement occurs on the transaction dates. Calculate the following using dollars and cents $($NOT percentages of face value$)$:

A$.$ The invoice price of the bond when you purchased it

B$.$ The invoice price of the bond when you sold it

C$.$ How much interest you earned for the time you held the bond

D$.$ How much interest you paid on the Repo $($you pay the entire amount when you receive the bond back $$ it is not paid each day $$ so consider compounding$)$

E$.$ The net gain or loss on the round$-$trip transaction