Answer:
To calculate the yield to maturity (YTM) of a bond, we need to use the formula for the present value of a bond:
�
=
�
(
1
+
�
)
1
+
�
(
1
+
�
)
2
+
…
+
�
(
1
+
�
)
�
+
�
(
1
+
�
)
�
P=
(1+r)
1
C
+
(1+r)
2
C
+…+
(1+r)
n
C
+
(1+r)
n
F
Where:
�
P = Market price of the bond ($977.00)
�
C = Coupon payment ($35.00, which is 7% of $1,000 par value)
�
r = Yield to maturity (what we're trying to find)
�
n = Number of periods (17.00 years, but since it's a semi-annual bond, it's
17
×
2
=
34
17×2=34 periods)
�
F = Par value of the bond ($1,000)
Now we'll plug in the given values and solve for
�
r:
977
=
35
(
1
+
�
)
1
+
35
(
1
+
�
)
2
+
…
+
35
(
1
+
�
)
34
+
1000
(
1
+
�
)
34
977=
(1+r)
1
35
+
(1+r)
2
35
+…+
(1+r)
34
35
+
(1+r)
34
1000
Since this equation involves a sum of terms, it's best to use financial calculators, spreadsheets, or specialized software to solve it. However, for manual calculation, we can use trial and error or iterative methods to approximate the YTM.
After calculating, the yield to maturity is approximately 3.62% (rounded to two decimal places).
