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Definition of Duration in financial mathematics Notes
The average time taken by a bond, on a discounted basis, to
pay back the original investment.
(Macaulay) Duration of a bond is the weighted average of
the maturity of individual cash flows, with the we
Future Value of a Lump Sum Notes
The future value in 2 years of $1,000 earning 5% annually is
an example of computing the future value of a lump sum.
We can compute this in any one of three ways:
Using a calculator programmed for financial math
Solve the
Multiple or unique yield rate Notes
Often when solving for the yield rate, we may be left with a
polynomial equation.
The problem with polynomial equations is that they are liable
to have several roots.
In Example 7.3, we have two possible answers for the
Effective Annual Rate Notes
An effective annual rate is an annual compounding rate.
When compounding periods are not annual, the rate can still
be expressed as an effective annual rate using the following:
A bank offers a certificate of deposit rate of 6%
Ordinary Annuity Versus Annuity Due Notes
The PV of an ordinary annuity is located one period before
the first annuity payment.
The PV of an annuity due is located on the same date as
the first annuity payment.
The FV of an ordinary annuity is located on
Discounted cash flow analysis Notes
So far, we have analyzed the present value of a regular
series of payments, such as coupon bonds, annuities
This approach can be extended to any pattern of cash
returns.
By obtaining the present value of any pattern of
Yield Curve and Term structure of interest rates Notes
Investor prefer short term investments, so must be
coerced into buying longer term rates with higher
interest rates.
A graphical depiction of the relationship between the
yield on bonds of the same cr
Spot Interest Rates Notes
Spot interest rate, rt, is the (annualized) interest rate for a
transaction between today, 0, and a future date, t.
rt is for payments only on date t.
rt is the average rate of interest between now and
date t.
rt is different for
PV of a Series of Non-Constant Cash Flows Notes
The PV of a series of non-constant cash flows is just the
sum of the individual PV equations for each cash flow.
Where the Cfis are a series of non-constant cash flows from
year 1 to year n.
Suppose some new
Perpetuity An Infinite Annuity Notes
A perpetuity is essentially an infinite annuity.
An example is an investment which costs you $1,000 today
and promises to return to you $100 at the end of each
forever!
What is your rate of return or the interest rate?