Transcript FNCE 3020 - Leeds School of Business

FNCE 4070
FINANCIAL
MARKETS
AND INSTITUTIONS
Professor Michael Palmer
University of Colorado at Boulder
Spring Semester 2011
Lecture 3: Understanding Interest Rates
Can you explain this?

Treasuries Decline as Weekly Jobless Claims
Drop

Treasuries declined as first-time claims for
unemployment insurance fell to the lowest since
July 2008.
Interest Rate Defined

“Dual” Definition:

Borrowing: the cost of borrowing or the price (%) paid
for the “rental” of funds.


Saving: the return from investing funds or the price
(%) paid to delay consumption.


A financial liability for “deficit” entities.
A financial asset for “surplus” entities.
Both concepts are expressed as a percentage
per year (Percent per annum – p.a.).

True regardless of maturity of instrument of the
financial liability or financial asset.


Thus, all interest rate data is annualized.
See: http://www.federalreserve.gov/releases/h15/update/
Savings and Borrowing Rates: They
Move Together, 1990 – 2010

Regression analysis: 1964 – 2010 (monthly data, 564 observations);
CD rate as dependent variable. R-squared = 88.55%
Commonly Used Interest Rate Measures

There are four important ways of measuring
(and reporting) interest rates on financial
instruments. These are:




Coupon yield: The “promised” annual percent return
on a coupon instrument.
Current Yield: Bond’s annual coupon payment divided
by its current market price.
Discount Yield and Investment Yield: The yield on Tbills (and other discounted securities, such as
commercial paper) which are selling at a discount of
their maturity values.
Yield to Maturity: The interest rate that equates the
future payments to be received from a financial
instrument (coupons plus maturity value) with its
market price today (i.e., to its present value).
Benchmarking with Interest Rates




Interest rates can be used for cross-country
assessments or changes in individual country
assessments over time.
The most common benchmark rates are yields
to maturity on 10-year Government U.S.
Treasuries and German Bunds.
We assume these are “default-free.”
Thus we can compare other sovereigns to these
(and to one another) to assess :





Credit ratings risk
Inflation risk
The market’s overall assessment of country risk
See next slide for benchmark data.
Source: http://markets.ft.com/markets/bonds.asp
FT Reported 10-Year Government
Benchmark Rates, February 8, 2011
Country
Latest
Spread
vs Bund
Spread vs
T-Bonds
Country
Latest
Spread
vs Bund
Spread vs
T-Bonds
US
3.66%
+0.41
0.00
Greece
11.21%
+7.96
+7.55
UK
3.84%
+0.59
+0.17
Germany 3.25%
0.00
-0.41
Switzerland
1.94%
-1.31
-1.73
France
3.64%
+0.38
-0.03
Sweden
3.46%
+0.21
-0.20
Finland
3.47%
+0.22
-0.19
Spain
5.31%
+2.05
+1.64
Denmark 3.31%
+0.05
-0.36
Portugal
7.23%
+3.97
+3.56
Canada
3.47%
+0.22
-0.19
New Zealand 5.57%
+2.31
+1.90
Belgium
4.24%
+0.99
+0.58
Netherlands
3.44%
+0.19
-0.22
Austria
3.71%
+0.46
+0.04
Japan
1.33%
-1.93
-2.34
Australia
5.72%
+2.46
+2.05
Coupon Yield



Coupon yield is the annual interest rate which was promised
by the issuer when a bond is first sold.
 Information is found in the bond’s indenture.
The coupon yield is expressed as a percentage of the bond’s
par value.
 Par value is also called the maturity value (or face value).
In the United States, all bonds have a par value of $1,000
(Government bonds called Treasuries).


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

UK Government bonds (£100 par value; called gilts)
Japanese Government bonds (¥10,000 par value; called JGBs)
German Government bonds (minimum amount of €100 par value,
called bunds)
Canadian Government bonds (CAD$1,000 par value)
If a U.S. bond has a stated coupon yield of 4.5%, this means
that it will pay the holder $45 per year (0.045 x $1,000).
The coupon yield on a bond will not change during the
lifespan of the bond.
Current Yield

Since bond prices are likely to change, we often
refer to the “current yield” which is measured by
dividing a bond’s annual coupon payment by its
current market price.



So, if our 4.5% coupon bond is currently selling
at $900 the calculated current yield is:


This provides us with a measure of the interest yield
obtained at the current market price (i.e., cost)
Current yield = coupon payment/market price
$45/$900 = 5.00%
And if the bond is selling at $1,100, the current
yield is:

$45/$1,100 = 4.09%
Discount and Investment Yield


Discount yields and investment yields are calculated
for T-bills and other short term money market
instruments (e.g., commercial paper and bankers’
acceptances) where there are no stated coupons
(and thus the assets are quoted at a discount of
their maturity value).
The discount yield relates the return to the
instrument’s par (or face or maturity) value.


The discount yield is sometimes called the bank discount
rate or the discount rate.
The investment yield relates the return to the
instrument’s current market price.

The investment yield is sometimes called the coupon
equivalent yield, the bond equivalent rate, the effective
yield or the interest yield.
Calculating the Discount Yield




Discount yield = [(PV - MP)/PV] * [360/M]
PV = par (or face or maturity) value
MP = market price
M = maturity of bill.



For a “new” three-month T-bill (13 weeks) use 91,
and for a six-month T-bill (26 weeks) use 182.
For outstanding issues, use the actual days to
maturity.
Note: 360 = is the number of days used by
banks to determine short-term interest rates.
Discount Yield Example


What is the discount yield for a 182-day T-bill,
with a market price of $965.93 (per $1,000
par, or face, value)?
Discount yield = [(PV - MP)/PV] * [360/M]
Discount yield = [(1,000) - (965.93)] / (1,000)
* [360/182]
Discount yield = [34.07 / 1,000] * [1.978022]
Discount yield = .0673912 = 6.74%
Investment Yield

The investment yield is generally calculated so
that we can compare the return on T-bills to
“coupon” investment options.



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The calculated investment yield is comparable to the
yields on coupon bearing securities, such as long term
bonds and notes.
As noted: The investment yield relates the return
to the instrument’s current market price.
In addition, the investment yield is based on a
calendar year: 365 days, or 366 in leap years.
Investment yield = [(PV - MP)/MP] * [365 or
366/M]
Investment Yield Example


What is the investment yield of a 182-day Tbill, with a market price of $965.93 per $1,000
par, or face, value?
Investment yield = [(PV - MP)/MP] * [365/M]
Investment yield = [(1,000 – 965.93) /
(965.93)] * [365/182]
Investment yield = [34.07] / 965.93] *
[2.0054945]
Investment yield = .0707372 = 7.07%
Comparing Discount and
Investment Yields

Looking at the last two examples we found:
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Note: The discount formula will tend to “understate” yields relative
to those computed by the investment method, because the market
price is lower than the par value ($1,000).



Discount yield = [(PV - MP)/PV] * [360/M]
Discount yield = [(1,000 - 965.93)] / (1,000) * [360/182]
Discount yield = [34.07 / 1,000] * [1.978022]
Discount yield = .0673912 = 6.74%
Investment yield = [(PV - MP)/MP] * [365/M]
Investment yield = [(1,000 – 965.93)] / (965.93) * [365/182]
Investment yield = [34.07 / 965.93] * [2.0054945]
Investment yield = .0707372 = 7.07%
However, if the market price is very close to the par value, the yields will be
similar.
See: http://www.ustreas.gov/offices/domestic-finance/debtmanagement/interest-rate/daily_treas_bill_rates.shtml
And: http://www.treasurydirect.gov/RI/OFBills
Bloomberg and Reported Yields on
T-Bills




Go to http://www.Bloomberg.com
Go to Market Data
Go to Rates and Bonds
You will see for “U.S. Treasuries” the following data (note:
this is an example from the Feb 4, 2011 site):
Coupon
3-month
6-month
12-month

0.000
0.000
0.000
Maturity
Date
05/05/2011
08/04/2011
01/12/2011
Current
Price/Yield
0.14/.15
0.16/.17
0.27/.28
Key: These are T-bills, thus the coupon is 0% (recall they
are sold at a discount). At maturity date they will pay the
holder $1,000. The current price is the discount yield (bank
discount yield) and the current yield is the investment yield
(bond or coupon equivalent yield).
Yield to Maturity



The yield to maturity uses the concept of present value
in its determination.
Yield to maturity is the interest rate at which if we
discount the incomes (i.e., cash-flows) of a bond, we get
the par value exactly (or the net present value = 0).
Yield to maturity (i) is calculated as:
C
C
C
C
PV
MP 


 ...

2
3
n
n
1  i  1  i  1  i 
1  i  1  i 


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
MP = Market price of a bond (i.e., present value)
C = Coupon payments (a cash flow)
PV = Par, or face value, at maturity (a cash flow)
n = Years to maturity
Note: i is also the internal rate of return
Yield to Maturity Example

Assume the following given variables:
C =$40 (thus a 4.0% coupon issue; paid annually)
N =10
PV =$1,000
MP =$1,050 (note: bond is selling at a premium of par)
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

1050 = 40/(1 + i)1 + 40/(1 + i)2 + . . . + 40/(1 + i)10
+ 1000/(1 + i)10
Solve for i, the yield to maturity
Note: The “i" calculated using this formula will be
the return that you will be getting when the bond
is held until it matures and assuming that the
periodic coupon payments are reinvested at the
same yield. In this example, the “i" is 3.4%.
Yield to Maturity Second Example

Now assume the following:

C =$40
N =10
PV =$1,000
MP =$900.00 (note: bond is selling at a discount of
par)

900 = 40/(1 + i)1 + 40/(1 + i)2 + . . . + 40/(1 + i)10 +
1,000/(1 + i)10

Solve for i, the yield to maturity

Note: The “i" calculated in this example is 5.315%.
What one factor accounts for the yield to maturity
difference when compared to the previous slide, with
its i of 3.4%?

Useful Web Site for Calculating a
Bond’s Yield to Maturity


While yields to maturity can be determined
through a book of bond tables or through
business calculators, the following is a useful
web site for doing so:
http://www.moneyzine.com/Calculators/InvestmentCalculators/Bond-Yield-Calculator/
The Yield to Maturity
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
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Think of the yield to maturity as the “required return
on an investment.”
Since the required return changes over time, we can
expect these changes to produce inverse changes in
the prices on outstanding (seasoned) bonds.
Why will the required return change over time?



Changes in inflation (inflationary expectations).
Changes in the economy’s credit conditions resulting from
change in business activity.
Changes in central bank policies.


Impact on shorter term maturities.
Changes in the credit risk (i.e., risk of default) associated with
the issuer of the bond.

On Governments, also changes in credit ratings risk

Portugal this week.
Illustrating the Relationship Between
Interest Rates and Bond Prices

Assume the following:


A 10 year corporate Aaa bond which was issued 8
years ago (thus it has 2 years to maturity) has a
coupon rate of 7%, with interest paid annually.
Thus, 7% was the required return when this bond was
issued.



This bond is referred to as an outstanding (or seasoned) bond.
Question: How much will a holder of this bond receive
in interest payments each year?
This bond has a par value of $1,000.

Question: How much will a holder of this bond receive in
principal payment at the end of 2 years?
What Happens when Interest Rates
Rise?

Assume, market interest rates rise (i.e., the required return rises)
and now 2 year Aaa corporate bonds are now offering coupon
returns of 10%.




This is the “current required return” (or “i” in the present value bond
formula)
Question: What will the market pay (i.e., market price) for the
outstanding 2 year, 7% coupon bond noted on the previous
slide?
 PV = $70/(1+.10) + $1,070/(1+.10)2
 PV = $947.94 (this is today’s market price)
Note: The 2 year bond’s price has fallen below par (selling at a
discount of its par value).
Conclusion: When market interest rates rise, the prices on
outstanding bonds will fall.
What Happens when Interest Rates
Fall?

Assume, market interest rates fall (i.e., the required return falls)
and now 2 year Aaa corporate bonds are now offering coupon
returns of 5%.


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This is the “current required return” (or “i” in the present value bond
formula)
Question: What will the market pay (i.e., market price) for the
outstanding 2 year, 7% coupon bond?
2
 PV = $70/(1+.05) + $1,070/(1+.05)
 PV = $1,037.19 (this is today’s market price)
Note: The 2 year bond’s price has risen above par (selling at a
premium of its par value).
Conclusion: When market interest rates fall, the prices on
outstanding bonds will rise.
Change in Market’s Required Return
Versus Change in Market Demand

The examples on the previous slides demonstrated
the impact of a change in the market’s required
return on bond prices.


Observation: Cause – effect relationship runs from
changes in required return to changes in market prices
(which produce the market’s new required return).
However, it is possible for a change in market
demand to produce changes in bond prices and
thus in market interest rates.


For example: Safe haven effects result in changes in
demand for particular assets.
Observation: Cause – effect relationship runs from
changes in demand to changes in prices (which have an
automatic impact on yields).
QE 2 Impacts on Interest Rates

How can we view QE2’s potential impact on long
term interest rates.


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Should the required return on longer-term, seasoned
issues change?
Probably not.
Two possible channels of influence:
(1) Demand and Supply of Bonds: Fed purchases
will drive up market prices (increase in demand),
and thus drive down yield, or Fed purchases will
reduce supply of long term securities, thus drive up
prices (and yields will fall).
(2) Demand and Supply of Loanable Funds:
Increase supply of long term funds will shift out the
supply (of loanable funds) schedule, thus push
down yields.
What if the Time to Maturity Varies?

Assume a one year bond (7% coupon) and the market
interest rate rises to 10%, or falls to 5%.



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
Now assume a two year bond (7% coupon) and the
market interest rate rises to 10%, or falls to 5%

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


PV@10% = $1,070/(1.10)
PV = $972.72
PV @5%= $1,070/(1.05)
PV = $1,019.05
PV@10% = $70/(1+.10) + $1,070/(1+.10)2
PV = $947.94
PV@5% = $70/(1.05) + $1,070/(1+.05) 2
PV = $1037.19
Conclusion: For a given interest rate change, the longer
the term to maturity, the greater the bond’s price change.
Summary: The Interest Rate Bond
Price Relationship

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#1: When the market interest rate (i.e., the required
rate) rises above the coupon rate on a bond, the
price of the bond falls (i.e., it sells at a discount of
par).
#2: When the market interest rate (i.e., the required
rate) falls below the coupon rate on a bond, the
price of the bond rises (i.e., it sells at a premium of
par)
IMPORTANT: There is an inverse relationship
between market interest rates and bond prices (on
outstanding or seasoned bonds).
#3: The price of a bond will always equal par if the
market interest rate equals the coupon rate.
Summary: The Interest Rate Bond
Price Relationship Continued

#4: The greater the term to maturity, the greater the
change in price (on outstanding bonds) for a given
change in market interest rates.


This becomes very important when developing a bond
portfolio-maturity strategy which incorporates expected
changes in interest rates.
This is the strategy used by bond traders:



What if you think interest rates will fall? Where should you
concentrate the maturity of your bonds?
What if you think interest rates will rise? Where should you
concentrate the maturity of your bonds?
See Appendix 1 for Excel Calculation of bond prices.
Interest Rate (or Price) Risk on a
Bond



Defined: The risk associated with a reduction in
the market price of a bond, resulting from a rise
in market interest rates.
This risk is present because of the “inverse”
relationship between market interest rates and
bond prices.
Greatest risk (i.e., potential price change) the
longer the maturity of the fixed income security
you are holding and the greater the interest rate
change.

For a historical example, see the next slide.
Illustration of Price Risk: 1950 - 1970
Reinvestment Risk on a Bond

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



Reinvestment risk occurs because of the need to “roll
over” securities at maturity, i.e., reinvesting the par value
into a new security.
Problem for bond holder: The interest rate you can
obtain at roll over is unknown while you are holding
these outstanding securities.
Issue: What if market interest rates fall?
You will then re-invest at a lower interest rate then the
rate you had on the maturing bond.
Potential reinvestment risk is greater when holding
shorter term fixed income securities.
With longer term bonds, you have locked in a known
return over the long term.

For a historical example, see the next slide
Illustration of Reinvestment Issue:
1990 - 2008
Concept of Bond Duration


Issue: The fact that two bonds have the same term to
maturity does not necessarily mean that they carry the
same interest rate risk (i.e., potential for a given change
in price).
Assume the following two bonds:



(1) A 20 year, 10% coupon bond and
(2) A 20 year, 6% coupon bond.
Which one do you think has the greatest interest rate
(i.e., price change) risk for a given change in interest
rates?

Hint: Think of the present value formula (market price of a bond)
and which bond will pay off more quickly to the holder (in terms of
coupon cash flows).
Solution to Previous Question




Assume interest rates change (increase) by 100
basis points, then for each bond we can
determine the following market price.
20-year, 10% coupon bond’s market price (at a
market interest rate of 11%) = $919.77
20-year, 6% coupon bond’s market price (at a
market interest rate of 7%) = $893.22
Observation: The bond with the higher coupon,
(10%) will pay back quicker (i.e., produces more
income early on), thus the impact of the new
discount rate on its cash flow is less.
Duration and Interest Rate Risk

Duration is an estimate of the average lifetime of
a security’s stream of payments.



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

Duration rules:
(1) The lower the coupon rate (maturity equal), the
longer the duration.
(2) The longer the term to maturity (coupon equal), the
longer duration.
(3) Zero-coupon bonds, which have only one cash
flow, have durations equal to their maturity.
Duration is a measure of risk because it has a
direct relationship with price volatility.
The longer the duration of a bond, the greater
the interest rate (price) risk and the shorter the
duration of a bond, the less the interest rate risk.
Calculated Durations

Duration for a 10 year bond assuming different
coupons yields:




Duration 6.54 yrs
Duration 7.99 yrs
Duration 10 years
Duration for a 10% coupon bond assuming
different maturities:




Coupon 10%
Coupon 5%
Zero Coupon
5 years
10 years
20 years
Duration 4.05yrs
Duration 6.54 yrs
Duration 9.00 yrs
Note: See Appendix 2 for Excel calculations
Using Duration in Portfolio
Management


Given that the greater the duration of a bond, the
greater its price volatility (i.e., interest rate risk), we
can apply the following:
(1) For those who wish to minimize interest rate risk,
they should consider bonds with high coupon
payments and shorter maturities (also stay away
from zero coupon bonds).


Objective: Reduce the duration of their bond portfolio.
(2) For those who wish to maximize the potential for
price changes, they should consider bonds with low
coupon payments and longer maturities (including
zero coupon bonds).

Objective: Increase the duration of their bond portfolio
The Real Interest Rate

Real interest rate:

This is the market (or nominal) interest rate that
is adjusted for expected changes in the price
level (i.e., inflation) and is calculated as follows:
irr = imr - pe
Where:
irr = real rate of interest (% p.a.)
imr = market (nominal) rate of interest (% p.a.)
pe = expected annual rate of inflation, i.e., the
average annual price level change over the
maturity of the financial asset (% p.a.)
Real Interest Rate Impacts on Borrowing
and Investing



We assume that real interest rates more accurately
reflect the true cost of borrowing and true returns to
lenders and/or investors.
 Assume: imr = 10% and pe = 12% then
 irr = 10% - 12% = -2%
When the real rate is low (or negative), there should be a
greater incentive to borrow and less incentive to lend (or
invest).
 Assume: Imr = 10% and pe = 1% then
 Irr = 10% - 1% = 9%
When the real rate is high, there should be less incentive
to borrow and more incentive to lend (or invest).
U.S. Real and Nominal Interest Rates: 1953-2007
3-41
Real Interest Rate as an Indicator
of Monetary Policy

The real interest rate (on the fed funds rate) is also
assumed to be a better measure of the stance of
monetary policy than just the market interest rate.
 Why: Real rate affects borrowing decisions.
 If the real rate is negative, or very low, monetary
policy is very accommodative and borrowing will
be encouraged.
 If the real rate high, monetary policy is very tight
and borrowing will be discouraged.
 A neutral monetary policy occurs when the real
rate is zero.
Example of Nominal Versus Real
Rate
Economic Background

U.S. experiences the 2000
“dot-com” stock market
crash and “terrorist- attack”
induced recession of 2001:


March 11, 2000 to October 9,
2002, Nasdaq lost 78% of its
value.
In response the Fed pushed
the fed funds rates to 1.0%
(levels not seen since the
1950s)
Nominal Fed Funds Rate
Real Fed Funds Rate
Real Rate Goes Negative
2003/04
Where is it today?

Effective Rate: ______
Go to:
http://www.bloomberg.com/a
pps/quote?ticker=FEDL01%3
AIND

Latest Inflation: ______
Go to:
http://www.bls.gov/bls/inflatio
n.htm

Your analysis of monetary
policy and credit conditions
in the economy?
Another Web Site for Calculating
Yields

Visit the web site below. It allows you to calculate the current
yield and yield to maturity for specific data you input on:
 Current Market Price
 Coupon Rate
 Years to Maturity

It also allows you to calculate present values.

Use this web site to test your understanding of the relationship
between bond prices and interest rates.
 See what happens to the calculated interest rates when you
change the bond price above and below the par value.
 Note the inverse relationship.

http://www.moneychimp.com/calculator/bond_yield_calculator.htm
Internet Source of Interest Rate Date

Historical and Current Data for U.S.


http://www.federalreserve.gov/releases/h15/update/
Real Time Data (U.S. and other major countries)
 http://www.bloomberg.com


Go to Market Data and then to Rates and Bonds
Other Countries:

Economist.com (both web source or hard copy)
Appendix 1
Using Excel to Calculate the Market
Price (Present Value) of a Bond
Using Excel to Calculate Bond Price




Go to Formulas in Microsoft Excel
Go to Financial
Go to Price
Insert Your Data:

Example for 20 year, 10% coupon bond with market rate of
11%:








Settlement: DATE(2009,2,1) Assume, Feb 1, 2009
Maturity: DATE(2029,2,1) Note: 20 years to maturity
Rate: 10% (this is the coupon yield)
Yld: 11% (this is the yield to maturity)
Redemption: 100 (this is the price per $100)
Frequency: 2 (assume interest is paid semi-annually)
Basis: 3 (this basis uses a 365 day calendar year)
Formula result (i.e., price per $100 face value) = 91.97694
(or $919.77)
Appendix 2
Using Excel to Calculate the Duration of
a Bond
Using Excel to Calculate Duration




Go to Formulas in Microsoft Excel
Go to Financial
Go to Duration
Insert Your Data:

Example for 10 year, 10% coupon bond with market
rate of 10%:







Settlement: DATE(2009,2,1) Assume, Feb 1, 2009
Maturity: DATE(2019,2,1) Note: 10 years to maturity
Rate: 10% (this is the coupon yield)
Yld: 10% (this is the yield to maturity)
Frequency: 2 (assume interest is paid semi-annually)
Basis: 3 (this basis uses a 365 day calendar year)
Formula result = 6.54266
Appendix 3
The Real Interest Rate during a period
of deflation
What if the Rate of Inflation is
Negative (i.e., Deflation)

Assume the following:
 imr



= 3% and pe = -2%
Then the calculated real rate would be:
irr = 3% - (-2%) = 5%
Issues:

1. What will be the economy’s incentive to borrow?


High or low.
2, What are the issues facing the central bank when the
economy is experiencing deflation?

How can borrowing be encouraged?
Appendix 4
Types of Debt Instruments and Lending
Terms
2 Basic Types of Debt Instruments

Discount Bond (Zero-coupon Bond):





A bond whose purchase price is below the face (or par) value of
the bond (i.e., at a discount)
The entire face (par) value is paid at maturity.
There are no interest payments.
U.S. Treasury bills are an example of a discount security (as is
commercial paper and bankers’ acceptances).
Coupon Bond:

A bond that pays periodic interest payments (stated as the
coupon rate) for a specified period of time after which the total
principal (face or par value) is repaid.
 In the United States and Japan, interest payments are
typically made every six months and in Europe typically once
a year.
 coupon bonds can sell at either a discount or premium (of par
value).
 These bonds are generally callable.


Issuer can “retire” them before their stated maturity date.
Why do you think they might do this?
Important Terms in Lending

(Loan) Principal: the amount of funds the lender provides
to the borrower.

Maturity Date: the date the loan must be repaid or
refinanced.

(Loan) Term: the time period from initiation of the loan to
the maturity date.

Interest Payment: the cash amount that the borrower
must pay the lender for the use of the loan principal.

(Simple) Interest Rate: the annual interest payment
divided by the loan principal.

In bond terminology, the coupon interest rate is the annual interest
payment divided by the par value.
Types of Loans

Simple Loan: Principal and all interest both paid at
maturity (i.e., date when loan comes due).



Borrow $1,000 today at 5% and in 1 year pay $1,050
Commercial bank loans to businesses are usually simply
loans.
Fixed-payment Loan: Equal monthly payments
representing a portion of the principal borrowed plus
interest. Paid for a set number of years, at which
time (maturity date) the principal amount is fully
repaid.


Referred to as an amortized loan.
Home mortgages (conventional), automobile loans.
Amortization Loan Example: Real
Estate

Mortgage Loan




Monthly Payment


$3,326.51 (for 360 months, i.e., 30 years)
First Month Payment (n = 1):


Principal Amount: $500,000
Years To Maturity: 30 years (with monthly payments)
Interest rate: 7% (fixed rate mortgage)
Principal: $409.84; Interest: $2,916.67 (or, $3,326.51)
Last Month Payment (n = 360):

Principal: $3,307.22; Interest: $19.29 (or, $3,326.51)
Appendix 5
Quoting Treasury Notes and Bonds
Treasury Prices in 32nds



Treasury note and bond prices are quoted in dollars and fractions
of a dollar.
By market convention, the normal fraction used for Treasury
security prices is 1/32 (of $1).
In a quoted price, the decimal point separates the full dollar
portion of the price from the 32nds of a dollar, which are to the
right of the decimal.



Thus a quote of 100.08 means $105 plus 8/32 of a dollar, or $100.25, for
each $100 face value of the note.
Note: the symbol + refers to ½ of 1/32nd.
Change data is the difference between the current trading day's
price and the price of the preceding trading day. It, too, is a
shorthand reference to 32nds of a point.

For example, a +16 refers to a change of 16/32 or 50 cents from the
previous day.