You observe the following market prices of zero$-$coupon bonds each with a face value of $$100$:

You also observe a $10\%$ government coupon bond with

Time to Maturity $($Years$)$ Price

$0\mathrm{.}598$

$1\mathrm{.}096$

face value of $10,000$ dollars, one year to maturity, paying semi$-$annual coupons. This bond has a market price equal to $$11,070.$

a$.$ Your friend claims that the market annual yield to maturity for the coupon paying bond is $4\mathrm{.}15\%.$ Is she correct?

b$.$ If transactions $($buying & selling$)$ can be executed at the prices reported above and you can buy or sell as many zero and coupon bonds as you need, is there an arbitrage opportunity? If so$,$ explain in detail how it can be earned. Be specific as to the amount and timing of cash flows $($i$.$e$.,$ show the cash inflows$/$outflows for each of the relevant maturity dates$).$