Saturday, June 04, 2005
13:34:10
1
Finding the Future Value of Interest
Rates
Geometric Mean Methodology
1.
Assumption:
Long Term Rates are based
on a series of short term rates
2.
The Present Value of a debt instrument is
based on the expected value of short
term interest rates in the future, i.e.,
1
2
3
,
1,.., ,
(1
)(1
)(1
)
(1
)
t
t
FV
PV
i
t
r
r
r
r
=
=
+
+
+
⋅⋅⋅
+
where r
t
equals the interest rate that will prevail in
time t and FV
t
is the future value of the debt
instrument in time t.
t
k
Eq. 1
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Saturday, June 04, 2005
13:34:10
2
Example: Present Value of a $1000 Debt
Instrument
Year
Expected
Interest Rates
0 (today)
8%
1
10%
2
11%
3
11%
FV
t
= $1000
PV
1
= $1000/(1.08) = $925.93
PV
2
= $1000/[(1.08)(1.10)] = $841.75
PV
3
= $1000/[(1.08)(1.10)(1.11)] = $758.33
PV
4
= $1000/[(1.08)(1.10)(1.11)(1.11)] = $638.18
Time to
Maturity
Present
Value
Yield to
Maturity
1
$925.93
2
$841.75
3
$758.33
4
$638.18
Saturday, June 04, 2005
13:34:10
3
Determining the Yield to Maturity
•
Yield to maturity means that for a multiyear debt
instrument you have to determine
one
interest rate for
all
years that is less than or equal to the expected
short term interest rate for each year.
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