The yield to maturity $($YTM$)$ on $1-$year zero$-$coupon bonds is $4\%$ and the YTM on $2-$year zeros is $5\%.$ The yield to maturity on $2-$year$-$

maturity coupon bonds with coupon rates of $9\%($paid annually$)$ is $4\mathrm{.}5\%.$

a$.$ What arbitrage opportunity is available for an investment banking firm?

The arbitrage strategy is to buy zeros with face values of

and

and respective maturities of one year and two years.

b$.$ What is the profit on the activity? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Profit

each bond

$2$ decimal places required.