A $1-$year government bond issued on Jan $1$st $2023$ promises to pay $100$ a year until

it matures on Jan $1$st $2024.$ The interest rate at issuance was $5\%$ per year.

$($a$)$ Find the bond price on Jan $1$st $2023($i$.$e$.$ the principal, or face value, of the bond$).$

$($b$)$ Suppose the interest rate on $1-$year government bonds rises on Jan $2$nd $2023,$ after

it is revealed that the government 'fiddled the books' to conceal a large budget deficit.

The interest rate paid on subsequent issuances of the $1-$year bond is $10\%$ per year.

What would you expect to happen to the resale price of the bond in $($a$)?$

$($c$)$ ABC Insurance purchased $10$ of the bonds described in $($a$).$ It has cash worth

$10,000$ and it owes insurance claims worth $25,000$ to its customers. Use this infor$-$

mation to complete the table below. Does ABC Insurance remain solvent? Explain.