Exercise 13.1
Exercise 13.1, Solution 1:
Face value,
FV
= $1000.00,
n
= 2
×
5 = 10,
Coupon rate,
b
=== 0.015 per half-year
PMT
=
FV
×
b
= 1000.00 × 0.015 = $15.00
Yield,
i
=== 0.0125 per half-year
purchase price = PV
PMT
+ PV
Face Value
=
+
=+ 1000(1+0.0125)
-10
= 140.182888… + 883.180926…
= $1023.363815… = $1023.36
Premium = Purchase Price – Face Value=1023.36 – 1000.00 = $23.36
Therefore, she paid $1023.36 for this bond, and the premium was $23.36.
Exercise 13.1, Solution 3:
Face value,
FV
= $25,000.00,
n
= 2
×
10 = 20,
Coupon rate,
b
=== 0.0225 per half-year
PMT
=
FV
×
b
= 25,000.00 × 0.0225 = $562.50
Yield,
i
=== 0.015 per half-year
purchase price = PV
PMT
+ PV
Face Value
=
+
=+ 25,000(1+0.015)
-20
= 9657.359317… + 18,561.76046…
= $28,219.11977… = $28,219.12
Premium = Purchase Price – Face Value=28,219.12 – 25,000.00 = $3219.12
Therefore, the issue price is $28,219.12, and the premium is $3219.12.
Exercise 13.1, Solution 5:
Face value,
FV
= $10,000.00,
n
= 2
×
3 = 6,
Coupon rate,
b
=== 0.0175 per half-year
PMT
=
FV
×
b
= 10,000.00 × 0.0175 = $175.00
Yield,
i
=== 0.00875 quarterly
c
=
Number of compounding periods per year
Number of payments per year
=
i
2
= (1 +
i
)
c
– 1 = (1 +
0.00875
)
(4/2)
– 1 = 0.017576… semi-annually
purchase price = PV
PMT
+ PV
Face Value
=
+
=+ 10,000(1+0.017576.
..)
-6
= 988.3180464… + 9007.358062…
= $9995.676109.
.. = $9995.68
Discount = Face Value – sale Price = 10,000.00 – 9995.68 = $4.32
Therefore, the purchase price is $9995.68, and the discount is $4.32.
Exercise 13.1, Solution 7:
Purchasing the bond
Face value,
FV
= $1000.00,
n
= 2
×
5 = 10,