Show me the steps to solve Question $1(15$p$)$

Consider a corporate bond. The par value is $$100,000$ with annual paying coupons. There are $4$

years until the bond matures. The coupon rate is $4\mathrm{.}5$ percent and the yield to maturity is $2\mathrm{.}2$ percent,

both on an annual basis. Answer the following questions. Show and explain all your answers and

calculations with words.

$($i$)$ Calculate the price of the bond. Is the bond selling at a premium or discount? Explain why.

$(5p)$

$P=108,715\mathrm{.}44$; Selling at a premium since coupon rate $(0\mathrm{.}045)$ higher than yield to maturity

$(0\mathrm{.}022)$

$($ii$)$ Calculate the Macaulay's duration on an annual basis. $(5$p$)$

Duration $=3\mathrm{.}76$

$($iii$)$ You expect that the annual interest rate will increase with $20$ basis points. How large is the

approximate change in bond price measured in percent and in US dollar. $(2$p$)$

Decrease in price with $-0\mathrm{.}74\%$ or $-800\mathrm{.}04$ USD

$($iv$)$ Assume that you buy the bond today and sell the bond two years later to the price $$104,200.$

What is your holding period return? $(3$ p $)$

$HPR=0\mathrm{.}0413(4\mathrm{.}13\%)$