Semiannual interest
Most bonds, although the coupon rate is stated
as an annual interest rate, actually pay interest
semiannually. Valuing bonds that pay interest
semiannually involves three steps:
 Convert bond's annual interest (I) to semiannual
interest  divide I by 2
 Convert the years to maturity (n) to semiannual
periods  multiply n by 2
 Convert annual required return (i) to semiannual
discount rate  divide i by 2
The bond valuation formula for a bond paying
interest semiannually is:
B_{0} = Sum (1 to n)
I/2 / (1+i/2)^{2n}
+ M/ (1+i/2)^{2n}
OR
B_{0} = I/2 *[(1+i/2)^{2n}
 1] / [(1+i/2)^{2n} * i/2]
+ M/ (1+i/2)^{2n} ^{ }

B_{0} 
= bond's value at time zero 
I 
= annual interest payments 
i 
= discount rate 
n 
= number of years to maturity 
M 
= par value (payment at maturity) 
Computing bond price. If
you know the bond's par value, coupon rate, time
to maturity and current yield, you can compute
its price. See attached
spreadsheet for computing prices and yields
for bonds paying semiannual interest.
Continuous compounding. [Example
of continuous compounding] 
Example
Returning to our example, suppose
Play Now issues tenyear bonds (par $1,000)
with an annual coupon rate of 8.6% that pay
interest semiannually. Similar tenyear
bonds are paying 8.0% interest. What is the
value of one of Play Now's new bonds  that
is, what should be its price?
Answer. You can
use present
value and present
value annuity tables:
B_{0} 
= 
C/2/(1+ i/2)^{2n} + M/(1+i/2)^{2n} 

= 
$43 x (PV of 20period $1 annuity at 4.0%
per period) + $1,000 x (PV of $1 after 20
periods at 4.0% per period 

= 
($43 x 13.590) + ($1,000 x .4564) 

= 
$584.37 + $456.40 

= 
$1,040.77 
Notice that this bond is identical
to the bond in the previous example with the
exception that it pays interest semiannually.
The effect of the semiannual payments is to
increase the price of the bond  from $1,040.26
to $1,040.77.
Answer. You
can also use a spreadsheet.
End of year 
Interest 
Principal 
Present value 
0.5 
$43 

$41.35 
1.0 
$43 

$39.76 
1.5 
$43 

$38.23 
2.0 
$43 

$36.76 
2.5 
$43 

$35.34 
3.0 
$43 

$33.98 
3.5 
$43 

$32.68 
4.0 
$43 

$31.42 
4.5 
$43 

$30.21 
5.0 
$43 

$29.05 
5.5 
$43 

$27.93 
6.0 
$43 

$26.86 
6.5 
$43 

$25.82 
7.0 
$43 

$24.83 
7.5 
$43 

$23.88 
8.0 
$43 

$22.96 
8.5 
$43 

$22.08 
9.0 
$43 

$21.23 
9.5 
$43 

$20.41 
10.0 
$43 

$19.62 
10.0 

$1000 
$456.39 


TOTAL 
$1,040.77 
