In January $2024,$ the yield on AAA rated corporate bonds averaged about $5$ percent; by the end of the year, the yield on these same bonds was about $7$ percent. Assume IBM issued a $10-$year, $5$ percent coupon bond on January $1,2024.$ On the same date, General Motors issued a $20-$year, $5$ percent coupon bond. Both bonds pay interest semi$-$annually. Also assume that the market rate on similar risk bonds was $5$ percent at the time the bonds were issued.

a$.$ Compute the market value of each bond at the time of issue. Show your work.

b$.$ Compute the market value of each bond one year after issue if the market yield for similar risk bonds was $7$ percent on January $1,2025.$ Show your work.

c$.$ Compute the $2024$ capital gains yield for each bond. Show your work.

d$.$ Compute the current yield for each bond in $2024.$ Show your work.

e$.$ Compute the total return each bond would have generated for investors in $2024.$ Show your work.

f$.$ If you invested in bonds at the beginning of $2024,$ would you have been better off to have held long$-$term or short$-$term bonds? Explain why. Show your work.

g$.$ Assume interest rates stabilize at the January $2025$ rate of $7\mathrm{.}0$ percent, and they stay at this level indefinitely. What would be the price of each bond on January $1,2030,$ after six years from the date of issue have passed? Describe what should happen to the prices of these bonds as they approach their maturities. Show your work.