Question

You purchase a bond with an invoice price of $1,210. The bond has a coupon rate of 4.6 percent, and there are 5 months to the next semiannual coupon date. What is the clean price of the bond? Assume a par value of $1,000.

Answer 1

Solution:

The formula for calculating the Clean Price of a bond is

Clean Price = Invoice Price - Accrued Interest

As per the information given in the question we have

Invoice Price= $ 1,210 ; Par value of bond = $ 1,000 ; Annual coupon rate = 4.6 %

No. of months for which the interest is accrued = 1 months

( Semi annual coupon payment is a payment for a period of 6 months. Since the coupon payment is due in five months, it implies that the accrued interest period = Total payment period – Due period

= 6 months – 5 months = 1 month )

Thus we have accrued Interest = ( Par value of bond * Annual coupon rate * No. of months for which the interest is accrued ) / 12

Applying the available information we have

Accrued Interest = ( $ 1,000 * 4.6 % * 1 ) / 12

= ( $ 46 * 1 ) / 12

= $ 46 / 12

= $ 3.8333

Thus Accrued Interest = $ 3.8333

Thus we have

Accrued Interest = $ 3.8333 ; Invoice Price = $ 1,210

Applying the above information in the formula for Clean price of a bond

= $ 1,210 - $ 3.8333

= $ 1,206.1667

= $ 1,206.17 ( when rounded off to two decimal places )

Thus the Clean price of the bond = $ 1,206.17