Consider a coupon bond with five years to maturity. The coupon rate is $8\%,$ and the

principal is $100.$ Do not use excel

$($a$)$ What is the present value at zero interest?

$($b$)$ What is duration at zero interest?

$($c$)$ What is duration at $5\%$ interest?

$($d$)$ Using the duration method, how much does the price change if the interest rate increases from $5\%$ to $6\%?$