In this problem we explore the difference between investing overnight $($so daily compound$-$

ing$)$ versus investing in a discount instrument, assuming both have the same quoted yield.

$($a$)$ Suppose you deposit $$1$M at the Fed $($or lend to the Federal Funds market$)$ at a $5\mathrm{.}00\%$

rate $($ACT$/360$ basis$).$ How much would be returned to you the following day?

$($b$)$ What if today is Friday? How much returned to you on Monday?

$($c$)$ After compounding, how much will you have by lending and rolling over for $1$ week

$($Friday to Friday$)?$

$($d$)$ Does it matter to how much we receive after lending for one week starting from another

day of the week $($Mon$,$ Tue, Wed or Thu$)?$

$($e$)$ How much do we have after $52$ weeks?

$($f$)$ In comparison, how much would we have if we invested $$1$M $($market value not face

value$)$ in $52-$week T$-$bills at a $5\mathrm{.}00\%$ yield?

$($g$)$ Which gives us more $($e$)$ or $($f$)?$ Can you explain why