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INTEREST RATE PROBLEM SET
YIELD FORMULAS
:
There are a number of different ways of calculating different yields.
A few
of these formulas are shown below.
1.
Current yield of a bond
:
annual coupon interest in dollars
= C
Current yield
=
Current Price
P
2.
Yield to maturity of a bond (r)
:
a.
Approximation formula:
Par Value  Current Price
coupon interest
+
n___________
Current Price +
Par Value
2
where n is the number of years to maturity and PV = par value
b.
Exact formula:
C
1
+
C
2
+ . . . . +
C
n + PV
Price=
(l + r)
(l + r)
2
(l + r)
n
Solve for r by trial and error.
3.
Treasury bill yields
:
a.
Discount yield (d):
d=
360
100  Price
n
100
where n is number of days to maturity; price is expressed in dollars per $100 of par value or
face amount.
b.
Equivalent bond or coupon yield (i):
I =
365
100  Price
n
Price
4.
Yield compounding
:
a.
Realized yield = (l + r/m)
m
 1 where
r = stated interest rate per year,
m = number of times interest is compounded per year.
b.
For continuous compounding:
Realized yield = e
r
 1
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Stock
:
a.
Constant Growth Model
P
o
=
D
1
K
e
 g
∞
b.
General Dividend Model
P
o
=
Σ
D
t
t=1
(1 + K)
t
m
c.
2 Period Growth Model
∑
D
o
(1 + g
1
)
t
+
I
1
D
m+1
I
t = 1
(1 + K
e
)
t
(1 + K
e
)
m
K
e
 g
2
ASSIGNMENT:
INTEREST RATES
This assignment explores several aspects of interest rates including (1) yield calculations, (2) yield
differentials, and (3) the term structure of yields.
Show all calculations.
1.
Find, in the (Date to be Announced), Wall Street Journal
, the close price for the American
Telephone and Telegraph (ATT) bond listed as
the "ATT 7 3/4 07."
The prices can be found in
the "US Bonds" section of the paper.
Assume that the bond matures in exactly
5
years.
a.
What is the dollar amount of interest paid on this bond each year?
b.
What is the bond's current yield?
c.
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This note was uploaded on 07/09/2011 for the course FIN 4504 taught by Professor Banko during the Summer '08 term at University of Florida.
 Summer '08
 BANKO
 Interest, Interest Rate

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