$1.$ Consider the following semiannual bond:

Coupon rate $=6\mathrm{.}5\%$

Maturity $=30$ years

Par value $=$ $$1,000$

Market price $=$ $$1,050$

Can be called in $10$ years at $$1,032\mathrm{.}5$

Can be called in $15$ years at par

Only put date in $20$ years and putable at par value

$(1)$ What is the yield to maturity for this bond?

$(2)$ What is the yield to first call?

$(3)$ What is the yield to second call?

$(4)$ What is the yield to worst for this bond?Consider the following semiannual bond:

Coupon rate $=6\mathrm{.}5\%$

Maturity $=30$ years

Par value $=$$$1,000$

Market price $=$$$1,050$

Can be called in $10$ years at $$1,032\mathrm{.}5$

Can be called in $15$ years at par

Only put date in $20$ years and putable at par value

$(1)$ What is the yield to maturity for this bond?

$(2)$ What is the yield to first call?

$(3)$ What is the yield to second call?

$(4)$ What is the yield to worst for this bond?