American Airlines is currently considering the issuance of a series of $$1,000$ par bonds. The coupon rate offered, based on current market interest rates and the Standard & Poor's based AMR bond rating, will be $10\%.$ The current interest rate is coincidentally $10\%$ as well. Interest on the bonds will be paid semiannually. However, American cannot decide on the maturity of the new issue. The life of the bonds will be $10,20,$ or $30$ years.

Questions

Ignoring floatation costs, what will the bonds sell for today if American decides to issue the bonds with a maturity of $10$ years? What will the price be if the bonds have a maturity of $20$ years? $30$ years?

If the bonds are issued with $10$ years to maturity and the day after they are issued, the market interest rates increase to $12\%,$ what will be the price of American Airline's bonds? What if interest rates drop to $8\%?$

If the bonds are issued with $20$ years to maturity and the day after they are issued, the market interest rates increase to $12\%,$ what will be the price of American Airline's bonds? What if interest rates drop to $8\%?$

If the bonds are issued with $30$ years to maturity and the day after they are issued, the market interest rates increase to $12\%,$ what will be the price of American Airline's bonds? What if interest rates drop to $8\%?$

Based on your answers to questions $2$ through $4,$ what is the relationship between time to maturity and the price of the bond?

Based on your answer to question $1,$ what is the relationship between current interest rates, the coupon rate, and time to maturity?

Forward Rates Problems

In December of $2022,$ the term structure of Treasury securities included the following rates:

$\backslash$table$[[$Security$,$Annualized Yield $(\%)],[3-$month bill,$4\mathrm{.}50],[6-$month bill,$4\mathrm{.}57],[1-$year note,$4\mathrm{.}52],[2-$year note,$4\mathrm{.}51],[3-$year note,$4\mathrm{.}48]]$

Questions

The six$-$month annualized yield expected in the second half of year $2023($forward rate for $6$month bill in June $2023)($see the table above$)$

The one$-$year expected yield for year $2025($forward rate for $1-$year note in December $2022)($see the table above$)$

Suppose the $8-$year spot interest rate is $8$ percent and the $3-$year spot rate is $4$ percent. What is the implied forward rate on a $5-$year bond originating $3$ years from now?

Suppose the $5-$year spot interest rate is $6$ percent. Under the expectation hypothesis the forward rate on a $3-$year bond originating $2$ years from now was estimated. The estimated forward rate is $5\mathrm{.}5$ percent. What is the $2-$year bond spot rate?