Answer:
The invoice price of the bond will be $100,127.88
Explanation:
Bonds are nothing but the debt instrument which a company uses to raise capital from the general public, these bonds can be of both short and long term period.
In the question it is given that bond has a coupon period of 182 days which means the bond is of short term period. Coupon rate of 7% means the bond gives the interest of 7% to its holder semiannually every year on January 15 and July 15.
It is given that the ask price for the bond on January 30 is 100.125 percent on par value of the bond which we are assuming to be $1000, which means the ask price is
$1000 X 100.125 = $100,125 ( ASK PRICE)
now we have to calculate the interest, remember the semiannually payment of interest has already been made on January 15 which means we have to find interest for only 15 days which will be taken out on par value
INTEREST = $1000 x 7% x 15 / 30
= $1000 x .07 x 1/ 2
= $35
INVOICE PRICE = INTEREST X \frac{TOTAL \: NUMBER \: OF \: DAYS}{COUPON \: PERIOD} + Ask price
= $35 X 15 / 182
= $2.884
Now adding this amount in to ask price
$100,125 + $2.884
= $100,127.88 ( INVOICE PRICE)
