Consider a bullet bond with principal $1000$ and annual coupon payments $70.$ Yield to

maturity is $5\%.$

$($a$)$ What is the price of the bond?

$($b$)$ Is this a premium bond or discount bond?

$($c$)$ What is the duration of the bond? Show your calculations, but you are encouraged

to check your answer against your calculator.

$($d$)$ Suppose the interest rate increases by a quarter from $5\%$ to $5\mathrm{.}25\%.$ According to the

duration method, what is the percentage change in the price of the bond?