Please answer Question #$2$

$(1)$ A bond will mature in $15$ years. It has a $4\%$ coupon rate and will pay annual

coupons. If the bond has a face value of $$1,000$ and a $4\mathrm{.}5\%$ yield to maturity,

what should be the price of the bond today? What if YTM goes up to $5\%?$ What

if YTM goes up to $5\mathrm{.}5\%?$

If the YTM of the bond is at $4\mathrm{.}5\%$

Step $1$: Calculate the Value of the bond

$FV$ of the bond $=1,000$

Term$(n)=15$ years

Rate $(r)=4\mathrm{.}50\%$

Coupon rate $=4\%$

Coupon amount $=$$$40$

Step $2$: Price of the bond

Formula to use

Price of the bond $=$ Coupon amount xPVAF$(r,n)+$ Face value amount xPVIF$(r,n)$

$$40$PVAF$(4\mathrm{.}50\%,15)+1,000$PVIF$(4\mathrm{.}50\%,15)$

$$4010\mathrm{.}7395457256+1,0000\mathrm{.}51672044225$

$429\mathrm{.}5818+516\mathrm{.}7204=$$$946\mathrm{.}30$

i$.$If YTM goes up to $5\%$

$$40$PVAF$(5\%,15)+1,000$PVIF$(5\%,15)$

$$4010\mathrm{.}3796580377+1,0000\mathrm{.}48101709804$

$415\mathrm{.}1863+481\mathrm{.}0171=$$$896\mathrm{.}20$

a$.$ If the bond is at $5\%$ the price of the bond today would $$896\mathrm{.}20$

ii$.$If the YTM does up to $5\mathrm{.}5\%$

$$40$PVAF$(5\mathrm{.}50\%,15)+1,000$PVIF$(5\mathrm{.}50\%,15)$

$$4010\mathrm{.}03758094+1,0000\mathrm{.}44793304806$

$401\mathrm{.}5032+447\mathrm{.}9330=$$$849\mathrm{.}44$

a$.$ If the bond goes up to $5\mathrm{.}5\%$ the price of the bond today would

$$894\mathrm{.}44$

$(2)$ What would be the price of the bond above in $(1)$ if the coupons were paid

semiannually?