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Title: Yield to Maturity
Description: These notes get into the particulars of how to calculate yield to maturity!! Learn how to calculate yield to maturity!!
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II

Unit VI Assignment Question 3
CSU Math Center | 1-800-977-8449 x6538 | teamsucceed@columbiasouthern
...
adobeconnect
...
What is the bond’s
yield to maturity?
Solution:
To find the YTM for this bond, we can use equation 9-2c, which accounts for semiannual
compounding:

1βˆ’
π΅π‘œπ‘›π‘‘ π‘‰π‘Žπ‘™π‘’π‘’ (π‘ π‘’π‘šπ‘–π‘Žπ‘›π‘›π‘’π‘Žπ‘™) = (

πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘
)
2
[

1
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ 2𝑛
(1 +
)
1
2
+ π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ [
]
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ 2𝑛
(1 +
)
2
2
]

πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ = π‘π‘œπ‘’π‘π‘œπ‘› π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ Γ— π‘π‘Žπ‘Ÿ π‘£π‘Žπ‘™π‘’π‘’
πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘ƒπ‘Žπ‘–π‘‘ βˆ’ π‘ π‘’π‘šπ‘–π‘Žπ‘›π‘›π‘’π‘Žπ‘™π‘™π‘¦
π‘ƒπ‘Žπ‘Ÿ π‘£π‘Žπ‘™π‘’π‘’ (π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ π΄π‘šπ‘œπ‘’π‘›π‘‘) = $1,000
πΆπ‘œπ‘’π‘π‘œπ‘› π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ = 8 % = 0
...
08 Γ— $1,000)
2
[

1
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ 2Γ—10
(1 +
)
1
2
+ $1,000 [
]
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ 2 Γ—10
(1 +
)
2
2
]

1βˆ’
$900 =

$80
2
[

1
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ 20
(1 +
)
1
2
+ $1,000 [
]
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘
π‘Œπ‘‡π‘€ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ 20
(1 +
)
2
2
]

The best way to solve for YTM is using the Excel’s RATE function
=RATE(nper, pmt, PV, FV) β†’ = RATE(10*2,80/2,-900,1000) β†’ = Rate = 0
...
0478807 βˆ— 2 = 0
...
πŸ“πŸ–%
Note, it’s not surprising the YTM is greater than the coupon rate
...
(Review the second
relationship in Section 9
Title: Yield to Maturity
Description: These notes get into the particulars of how to calculate yield to maturity!! Learn how to calculate yield to maturity!!
Buy These NotesPreview