Duration problem I

A bond makes annual coupon payments at rate $5\%,$ there are three remaining coupon

payments, and yield to maturity is $8\%.$

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

$($b$)$ Suppose the yield suddenly drops to $6\%.$ How large is the change in the bond price

according to duration?

Duration problem II

Consider a perpetuity with annual coupon rate $C=50.$

$($a$)$ If the interest rate is $5\%,$ what is the bond price?

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

$($c$)$ If the interest rate increases by one percentage point $($from $5\%$ to $6\%),$ exactly how

large is the change in the bond price?

$($d$)$ If the interest rate increases by one percentage point $($from $5\%$ to $6\%),$ how large is

the change in the bond price using duration to approximate the price change?