Calculating a Bond’s Accrued Interest

Although a semi-annual coupon bond will make an interest payment every six months, the investor who holds the bond will earn interest every day. Between payments interest accrues to the owner. When a bond is traded in the secondary market, the buyer pays the seller the current market value (clean price) of the bond plus any accrued interest. Accrued interest can be calculated from the following formula:

The sum of the bond’s market value (clean price) and accrued interest is called the bond’s full, or dirty, price.

Consider the following example: Calculate both the clean price and dirty price of a semi-annual coupon bond with a $1,000 face value, a 5% required rate of return, a 7% coupon rate, and six years remaining until maturity. There are 47 days remaining in the 182-day periodic payment interval.

Questions:

1.  Calculate the full price of a semi-annual coupon bond with a $1,000 face value, a 4% required rate of return, a 7% coupon rate, and six years remaining until maturity. There are 27 days remaining in the 182-day periodic payment interval.

2.  Calculate the full price of an annual coupon bond with a $10,000 face value, a 12% discount rate, a 10% coupon rate, and four years remaining until maturity. There are 200 days remaining in the 365-day periodic payment interval.
 

Answers:

1. $1,163.82          N = 12; I = 2; PMT = $35; FV = $1,000; PV = Solve
                           PV (Clean Price) = $1,158.63; Accrued Interest = $5.19
                           Full Price = $1,158.63 + $5.19 = $1,163.82

2. $9,392.53          N = 4; I = 12; PMT = $1,000; FV = $10,000; PV = Solve
                      PV (Clean Price) = $9,392.53; Accrued Interest = $547.95
                      Full Price = $9,392.53 + $547.95 = $9,940.48
 

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