Question $3(20$ points$)$

A bond pays a fixed coupon of $6\%$ p$.$a$.$ quarterly in arrears and is re$-$ deemed at $102\%.$ An investor who pays income tax $20\%$ and capital gains tax at $25\%$ is considering $100$ EUR nominal of the bond.

$(1)$ Calculate the price the investor should pay if the bond is redeemed after $10$Y so as to obtain a net yield of $($i$)8\%$ p$.$a$.$ effective $($ii$)10\%$ p$.$a$.$ effective.

$(2)$ The investor purchases the bond for price of i$)100$ eur ii$)112$ eur and redeems the bond after $10$ years. Estimate, using the linear interpolation, the net yield achieved in both cases.