Question $1$: A bond $($with a face value of $$1,000)$ was sold with a $12\%$ coupon rate with a maturity of exactly $25$ years. If the yield to maturity is $9\%($compounded semi$-$annually$),$ what is the price of the bond today? What is the bond$$s current yield?

Question $2$: Assume a fixed income security $($e$.$g$.$ a bond$),$ which has a face value of $$1,000,$ has a $9\%$ annual coupon rate $($it pays coupons semi annually$),$ and a remaining maturity of $20$ years. If the security is trading at a price of $$582\mathrm{.}64,$ what is the bond$$s yield to maturity? What is the bond$$s current yield? What is the bond$$s capital gain $($or loss$)$ yield?

Question $3$: Answer the following questions given the information below about your employment history and your future cash needs $($assuming a $10\%$ discount rate throughout$)$:

Today is your $25$th birthday, and starting exactly $1$ year after you were born, your grandmother deposited $$1,000$ into an account on your birthday $($including today, your $25$th birthday$)$ this is the last of those deposits. On your $22$nd birthday, you added $$5,000$ to the account and have added $8\%$ more on each birthday $($including your $25$th birthday, this year$)$ this is the last of those deposits. In addition, you are going to begin depositing $$50,000($beginning today $$ your $25$th birthday$)$ into this account. You will deposit this constant amount each year $($beginning today$)$ for the next $28$ years $($that is$,$ today plus $28$ more deposits$).$ Exactly $3$ years after the last deposit, you want to withdraw a constant amount per year for a total of $30$ years $($that is$,$ there will be $30$ total withdrawals$).$

If you want a zero balance in your account immediately after the last withdrawal what is the amount of each of the constant amounts being withdrawn?