Principles of Financial Market

CHAPTER 6: INTEREST RATE

1
OBJECTIVES

 Understand principles of interest rate and

Fisher equation
 Understand and apply methods of valuating
interest rate
 Understand factors affecting interest rate

 Understand principles of interest rate „s term

and risk structure
1. DEFINITION

 Interest rate is the price of using a unit of

loan (usually money) over a given period of
time.
2. CLASSIFICATION

2.1. Based on banking business:

 Deposit rate (saving rate)

 Rate for loan (borrowing rate)

 Discount rate

 Rediscount rate

 Interbank interest rate

 Basic interest rate

2. CLASSIFICATION

2.2. Based on the value of interest:

 Nominal interest rate: The interest rate
account for the nominal value of the
currency, not including the inflation rate.
Often published officially in credit contracts or
on debt instruments.
 Real interest rate: the interest rate adjusted
by change in expected inflation rate.
2. CLASSIFICATION
2.2. Based on the value of interest : (cont.)
 The relationship between nominal and real
interest rate is expressed by Fisher equation:
i = ir + πe
Where, i: nominal interest rate
ir : real interest rate
πe : expected inflation rate(*)
 When real iterest rate is low, borrower will have
more incentive to borrow and lender will have
less incentive to lend
2. CLASSIFICATION
2.3. Based on the flexibility of interest rate:
 Fixed rate
 Floating rate
2.4. Based on types of currency for lending:
 Domestic currency interest rate
 Foreign currency interest rate
2.5. Based on the credit source:
 Domestic rate
 International rate
3. VALUATING INTEREST RATE

3.1. Instruments of credit market:

3.1.1. Simple loan: A loan as a borrower will
pay the lender the principal and an interest
as the cost of using the loan at maturity..
Example: borrow 100mil for 1 year, 10%/yr
borrowing rate. After 1 year, you have to pay
110mil (100mil as the principle and 10mil as
interest)
3.1. INSTRUMENTS OF CREDIT MARKET

3.1.2. Fixed repayment loan: is the loan

method by which the borrower repays the
loan by paying the fixed amount after a fixed
period of time throughout the loan period.
Example: you borrow the bank 1bil to buy
house for 15 years and each year you have
to repay the bank 150mil (including part of
principle and interest)
3.1. INSTRUMENTS OF CREDIT MARKET

3.1.3. Coupon bond: Bond that pay interest as

a coupon periodically until the maturity. At
maturity, the bondholder will receive the face
value of the bond
Example: Tinh Viet bond has a face value of
100tr, 10%/yr coupon rate, paid annually.
3.1. INSTRUMENTS OF CREDIT MARKET

3.1.4. Discound bond (zero coupon bond): a

bond is sold at a price lower than the face
value. At maturity, the bondholder will receive
the face value. This kind of bond does not
pay coupon.
Example: Treasury bond has a face value of
10mil, sold at a price of 9mil, 1 year maturity.
VALUATING INTEREST RATE – TIME VALUE OF MONEY

Which would you prefer -- $10,000

today or $10,000 in 5 years?

Obviously, $10,000 today.

You already recognize that there is

TIME VALUE TO MONEY!!
WHY TIME?

Why is TIME such an important

element in your decision?

TIME allows you the opportunity to

postpone consumption and earn
INTEREST.

Other factors: inflation, risk

3. VALUATING INTEREST RATE
3.2Time value of money:
3.2.1. Simple interest:
 The interest rate is calculated on the principal only. The
interest is not included to the principle to calculate interest
for the next period.
 Used for credit contract with 1 year maturity or shorter.
 Since simple rate is usually in the form of % per annum,
you want to calculate the interest rate for a given term,
first calculate the term in how much part of a year then
multiply it with the simple rate.
For example: if the simple rate is 16%/yr then the simple
rate for 2-year is 32%, 6-month is 8%.
SIMPLE INTEREST FORMULA

Formula SI = P0(i)(n)

SI: Simple Interest

P0: Deposit today (t=0)
i: Interest Rate per Period
n: Number of Time Periods
SIMPLE INTEREST EXAMPLE

 Assume that you deposit $1,000 in an

account earning 7% simple interest for 2
years. What is the accumulated interest at
the end of the 2nd year?
 SI = P0(i)(n)
= $1,000(.07)(2)
= $140
SIMPLE INTEREST (FV)

 What is the Future Value (FV) of the

deposit?
FV = P0 + SI
= $1,000 + $140
= $1,140
 Future Value is the value at some future time
of a present amount of money, or a series of
payments, evaluated at a given interest rate.
SIMPLE INTEREST (PV)

 What is the Present Value (PV) of the

previous problem?
The Present Value is simply the
$1,000 you originally deposited.
That is the value today!
 Present Value is the current value of a
future amount of money, or a series of
payments, evaluated at a given interest
rate.
3. VALUATING INTEREST RATE
3.2. Time value of money :
3.2.2. Compound interest
Example:
a. A customer buy a bond with 2-year maturity,
12%/year compound interest rate. Interest is
paid each 6-month. What is the future value
the customer receive?
b. If you want to have 1bil after 30 years, how
much you have to save today. Known that the
compound interest rate of the bank is
10%/year.
 WHY COMPOUND INTEREST?

Future Value of a Single $1,000 Deposit

Future Value (U.S. Dollars)

20000
10% Simple
15000 Interest
7% Compound
10000
Interest
5000 10% Compound
Interest
0
1st Year 10th 20th 30th
Year Year Year
FUTURE VALUE
SINGLE DEPOSIT (GRAPHIC)

Assume that you deposit $1,000 at a

compound interest rate of 7% for 2 years.

0 1 2
7%

$1,000
FV2
 FUTURE VALUE
SINGLE DEPOSIT (FORMULA)

FV1 = P0 (1+i)1 = $1,000 (1.07)

= $1,070
Compound Interest
You earned $70 interest on your $1,000
deposit over the first year.
This is the same amount of interest you
would earn under simple interest.
Future Value
Single Deposit (Formula)

FV1 = P0 (1+i)1 = $1,000 (1.07)

= $1,070
FV2 = FV1 (1+i)1
= P0 (1+i)(1+i) = $1,000(1.07)(1.07)
= P0 (1+i)2 = $1,000(1.07)2
= $1,144.90
You earned an EXTRA $4.90 in Year 2 with
compound over simple interest.
GENERAL FUTURE VALUE FORMULA

FV1 = P0(1+i)1
FV2 = P0(1+i)2
etc.
General Future Value Formula:
FVn = P0 (1+i)n
3. VALUATING INTEREST RATE
3.2. Time value of money:
3.2.2. Compound interest:
 When loan contract has multiple periods of interest, the interest accrued
in the preceding period is added to the principal for interest calculation
for the next period, the method of calculating such interest is called the
compound interest rate.
 Usually applied for long term contract (longer than 1 year)
 Formula:
FV = PV x (1 + i/n)n.t
FV= PV.(1+i)n
CI= PV(1+i)n – PV = PV[(1+i)n-1]

Where,
P: present value
FV: future value
i: compound interest rate (%/year)
t: the maturity in term of year
n: the number of periods interest paid in one year
EXERCISE 1
In early 2017, Mr. Tony saved VND 50 million
for a 12-month term. Interest rate announced
by the bank is 8%. How much money will
Tony get by the end of 2022? Same at the
end of 2025? (Assuming Tony's deposit is
automatically renewed).
DOUBLE YOUR MONEY!!!

Quick! How long does it take to double

$5,000 at a compound rate of 12% per
year (approx.)?

We will use the “Rule-of-72”.

THE “RULE-OF-72”

Quick! How long does it take to double

$5,000 at a compound rate of 12% per
year (approx.)?

Approx. Years to Double = 72 / i%

72 / 12% = 6 Years
[Actual Time is 6.12 Years]
EXERCISE 3
 Ms Hang deposits 100 million VND in saving
account, term: 3 months. Calculating the
amount Ms Hang has after one year. The
bank's interest as follows:
Term Interest
1 month 12%
3 Months 13.20%
6 Months 15.60%
12 Months 16.80%
COMPOUNDING PERIOD (KỲ GHÉP LÃI )

The compound period is the time for the

arising interest to be added to the principal
and continue to calculate interest for the
subsequent period.
 VD: Deposit $1000 in bank, interest rate is
12%/year, compounding period is 6
months. What is the interest depositor
receive in this case?
EXERCISE 4
 Ms. Hang wants to buy an Emerald
apartment in Thu Duc. Real estate
consultant for Ms. Hang 2 payment options
as follows:
(1) Paying immediately 600 million, 2 years
after paying 240 million each year.
(2) Paying 1 billion immediately
The interest rate is 14%/year, other conditions
are the same. Please advise Ms Hang of
better option.
EXERCISE 5

(a) Winning a jackpot lottery prize immediately

get 1.5 billion
(b) Receive 150 million a year for 20 years.
Suppose the interest rate is 8% / year
Compare the two options?
3. VALUATING INTEREST RATE
3.2. Time value of money :
3.2.3. Effective interest rate:
 The real interest rate arises in a year, depending on
the nominal interest rate stated in the contract and
the number of period interest paid in one year
 Formula:
ief = (1+i/n)n -1
Where,
ief: effective interest rate (%/year)
i : nominal interest rate(%/year)
Example: Calculate the effective interest rate if the
interest is paid each 6-month, 3-month, 1-month known
that the nominal interest rate stated in the contract is
12%/year.
3.3.1. Yield to maturity of simple loan:
- For compound interest: yield to maturity
equal to nominal interest rate of the loan.
- For simple interest:
(1 + i.t) = (1 + i*)
Where,
i: nominal interest rate
i*: yield to maturity
3. VALUATING INTEREST RATE

3.3. Yield to maturity (YTM)

An interest rate that makes the present
value of future income (including principal
an interest) equal to the price of an
instrument.
3. VALUATING INTEREST RATE

3.3. Yield to maturity:

3.3.2. Yield to maturity of fixed repayment loan:
P = C/i* x [ 1 – 1/(1+i*)t ]
Where,
P: present value
C: fixed repayment annually
i*: yield to maturity
t: maturity
3. VALUATING INTEREST RATE

3.3. Yield to maturity:

3.3.2. Yield to maturity of coupon bond:
P = C/i* x [ 1 – 1/(1+i*)t ] + FV/(1+i*)t
Where,
P: price of bond (present value)
C: coupon
i*: yield to maturity
t: maturity
FV: face value of bond
 YTM OF A COUPON BOND

Maturity
YTM
1 2 3 4 5 6 7 8 9 10

8.50% 100.46 100.89 101.28 101.64 101.97 102.28 102.56 102.82 103.06 103.28

8.75% 100.23 100.44 100.64 100.81 100.98 101.13 101.27 101.40 101.51 101.62

9% 100 100 100 100 100 100 100 100 100 100

9.25% 99.77 99.56 99.37 99.19 99.03 98.89 98.75 98.63 98.52 98.41

9.50% 99.54 99.13 98.75 98.40 98.08 97.79 97.53 97.28 97.06 96.86

9.75% 99.32 98.69 98.13 97.61 97.14 96.71 96.32 95.96 95.64 95.34
3. VALUATING INTEREST RATE

3.3. Yield to maturity:

3.3.2. Yield to maturity of coupon bond :
 Perpeptuity:
i* = C/P
 Note: nominal rate of bond calculated as
follow
i = C/FV
3. VALUATING INTEREST RATE
3.3. Yield to maturity:
3.3.3. Yield to maturity of zero coupon bond
(discounted bond):

FV = P (1 + i*)t
Where,
FV: face value of bond
P: discounted price of bond
i*: yield to maturity
t: maturity
 Which of the following $1,000 face-value
securities has the highest yield to maturity?
a) A 5 percent coupon bond with a price of $600
b) A 5 percent coupon bond with a price of $800
c) A 5 percent coupon bond with a price of $1,000
d) A 5 percent coupon bond with a price of $1,200
 June would like to accumulate $70,000 by the
time her son starts college in ten years. What
amount would she need to deposit now in a
deposit account earning 6%, compounded
yearly, to accumulate her savings goal?

A. $4,200
 B. $39,513
 C. $39,088
 D. $125,359
 The relationship between nominal and real
interest rate is expressed by Fisher equation:
i = ir + πe
Where, i: nominal interest rate
ir : real interest rate
πe : expected inflation rate(*)
 When real interest rate is low, borrower will
have more incentive to borrow and lender will
have less incentive to lend
If you expect the inflation rate to be 4 percent
next year and a one year bond has a yield to
maturity of 7 percent, then the real interest rate
on this bond is
 A. -3 percent.

 B. -2 percent.

 C. 3 percent.

 D. 7 percent.
 Principles of Financial Market

CHAPTER 6: INTEREST RATE (CONT.)

BASIC FACTORS AFFECTING INTEREST RATE

45
1. LOANABLE FUNDS FRAMEWORK

 Analyzing loanable funds framework is also

referred to analyze bond demand and supply.
 Assume that there is only one kind of bond in
the market (discounted bond for 1 years)
1. LOANABLE FUNDS FRAMEWORK
1.1. Demand curve:
 Apply asset demand theory to analyze bond
demand.
 When interest rate increases (expected interest
rate), bond demand increase.
 The price of bond is opposite to interest rate,
bond demand increases when price decreases
(interest rate increases).
 Demand cure is a down curve.
FOR EXAMPLE
Demand Supply
Face value Interest rate
Price (USD) (billions of (billions of
(USD) (%)
USD) USD)
1000 950 ? 100 500
1000 900 ? 200 400
1000 850 ? 300 300
1000 800 ? 400 200
1000 750 ? 500 100
FOR EXAMPLE
Demand Supply
Face value Interest rate
Price (USD) (billions of (billions of
(USD) (%)
USD) USD)
1000 950 5,26 100 500
1000 900 11 200 400
1000 850 17,65 300 300
1000 800 25 400 200
1000 750 33,33 500 100
1. LOANABLE FUNDS FRAMEWORK

1.2. Supply curve:

 When interest rate decreases or price
increases, bond supply increases. Thus, the
supply curve is upward.
BOND DEMAND CURVE
BOND SUPPLY CURVE
MARKET EQUILLIBRIUM
1. LOANABLE FUNDS FRAMEWORK
1.3. Market equillibrium:
 Market is equilibrium when bond demand and
supply are equal
 For example: in the previous example, market
equilibrium when bond demand and supply are
equal at 300 tỷ USD. The interest rate at this
point is 17,65%. The equilibrium price is 850
USD
 Besides the market equilibrium, market maybe
in case of excess supply or excess demand.
2. FACTORS AFFECTING INTEREST RATE

 When bond demand (supply) changes

because of changes in bond price (interest
rate), the equilibrium move along the curve.
 When bond demand (supply) changes
because of other factors than changes in
bond price (interest rate), we have shifts in
demand or supply curve
2. FACTORS AFFECTING INTEREST RATE
DỊCH CHUYỂN ĐƯỜNG CUNG TRÁI PHIẾU
2. FACTORS AFFECTING INTEREST RATE

2.3. Apply different factors together in analyzing

interest rate equillibrium:
- Change in expected inflation (Fisher effect):
when expected inflation rate increases, interest
rate will increase.
- In the growth phase of economy: the equilibrium
quantity of bonds will increase. However,
interest rate increases or decreases depending
on how much demand curve and supply curve
change.
3. LIQUIDITY PREFERENCE THEORY

 In this theory, equilibrium interest rate is

defined by supply and demand of money
(cash).
 Main assumption: people use only two main
assets: bond and cash as reservation.
 Money does not have return and bond has
return rate equal to interest rate.
 Money supply is controlled by Central Bank.
3. LIQUIDITY PREFERENCE THEORY
3.1. Changes in equilibrium interest rate:
- Shift in money demand curve:
+ Increase in wealth will lead to increase in
money demand (money demand curve will shift
right)
+ Increase in price level will lead to increase in
money demand (money demand curve will shift
right)
- Shift in money supply curve: based on decision
of Central Bank
3. LIQUIDITY PREFERENCE THEORY

3.2. Apply theory to analyze change of equilibrium

interest rate:
- Change in income: equilibrium interest rate will
increase when income increases (in economic
growth phase, other factors unchanged)
- Chnge in price level: equilibrium interest rate will
increase when price level increases
- Chnge in money supply: equilibrium interest rate
will decrease when money supply increases.
3. LIQUIDITY PREFERENCE THEORY
3.3. Effects of increasing in money supply on interest
rate:
“Increase in money supply will always lead to the
decrease in interest rate?” Right or Wrong
 We will use four following effects to analyze the effect
of increasing in money supply on interest rate:
- Liquidity effect
- Income effect
- Price level
- Expected inflation effect
3. LIQUIDITY PREFERENCE THEORY
3.3. Effects of increasing in money supply on interest
rate (cont.):
 We will have three following cases:
- Liquidity effect is larger than other effects
- Liquidity effect is lower than other effects and
expected inflation effect is adjusted slowly
- Liquidity effect is lower than expected inflation effect
and expected inflation effect is adjusted quickly
 Recent research stated that increase in money
supply will lead interest rate decrease in short term
 Principles of Financial Market

CHAPTER 6: INTEREST RATE (CONT.)

BASIC FACTORS AFFECTING INTEREST RATE

64
1. LOANABLE FUNDS FRAMEWORK

 Analyzing loanable funds framework is also

referred to analyze bond demand and supply.
 Assume that there is only one kind of bond in
the market (discounted bond for 1 years)
1. LOANABLE FUNDS FRAMEWORK
1.1. Demand curve:
 Apply asset demand theory to analyze bond
demand.
 When interest rate increases (expected interest
rate), bond demand increase.
 The price of bond is opposite to interest rate,
bond demand increases when price decreases
(interest rate increases).
 Demand cure is a down curve.
FOR EXAMPLE
Demand Supply
Face value Interest rate
Price (USD) (billions of (billions of
(USD) (%)
USD) USD)
1000 950 5,26 100 500
1000 900 11 200 400
1000 850 17,65 300 300
1000 800 25 400 200
1000 750 33,33 500 100
1. LOANABLE FUNDS FRAMEWORK

1.2. Supply curve:

 When interest rate decreases or price
increases, bond supply increases. Thus, the
supply curve is upward.
BOND DEMAND CURVE
BOND SUPPLY CURVE
MARKET EQUILLIBRIUM
1. LOANABLE FUNDS FRAMEWORK

1.3. Market equillibrium:

 Market is equilibrium when bond demand and
supply are equal
 For example: in the previous example, market
equilibrium when bond demand and supply are
equal at 300 tỷ USD. The interest rate at this
point is 17,65%. The equilibrium price is 850
USD
 Besides the market equilibrium, market maybe
in case of excess supply or excess demand.
2. FACTORS AFFECTING INTEREST RATE

 When bond demand (supply) changes

because of changes in bond price (interest
rate), the equilibrium move along the curve.
 When bond demand (supply) changes
because of other factors than changes in
bond price (interest rate), we have shifts in
demand or supply curve
2. FACTORS AFFECTING INTEREST RATE
DỊCH CHUYỂN ĐƯỜNG CUNG TRÁI PHIẾU
2. FACTORS AFFECTING INTEREST RATE

2.3. Apply different factors together in analyzing

interest rate equillibrium:
- Change in expected inflation (Fisher effect):
when expected inflation rate increases, interest
rate will increase.
- In the growth phase of economy: the equilibrium
quantity of bonds will increase. However,
interest rate increases or decreases depending
on how much demand curve and supply curve
change.
3. LIQUIDITY PREFERENCE THEORY

 In this theory, equilibrium interest rate is

defined by supply and demand of money
(cash).
 Main assumption: people use only two main
assets: bond and cash as reservation.
 Money does not have return and bond has
return rate equal to interest rate.
 Money supply is controlled by Central Bank.
3. LIQUIDITY PREFERENCE THEORY
3.1. Changes in equilibrium interest rate:
- Shift in money demand curve:
+ Increase in wealth will lead to increase in
money demand (money demand curve will shift
right)
+ Increase in price level will lead to increase in
money demand (money demand curve will shift
right)
- Shift in money supply curve: based on decision
of Central Bank
3. LIQUIDITY PREFERENCE THEORY

3.2. Apply theory to analyze change of equilibrium

interest rate:
- Change in income: equilibrium interest rate will
increase when income increases (in economic
growth phase, other factors unchanged)
- Chnge in price level: equilibrium interest rate will
increase when price level increases
- Chnge in money supply: equilibrium interest rate
will decrease when money supply increases.
3. LIQUIDITY PREFERENCE THEORY
3.3. Effects of increasing in money supply on interest
rate:
“Increase in money supply will always lead to the
decrease in interest rate?” Right or Wrong
 We will use four following effects to analyze the effect
of increasing in money supply on interest rate:
- Liquidity effect
- Income effect
- Price level
- Expected inflation effect
3. LIQUIDITY PREFERENCE THEORY
3.3. Effects of increasing in money supply on interest
rate (cont.):
 We will have three following cases:
- Liquidity effect is larger than other effects
- Liquidity effect is lower than other effects and
expected inflation effect is adjusted slowly
- Liquidity effect is lower than expected inflation effect
and expected inflation effect is adjusted quickly
 Recent research stated that increase in money
supply will lead interest rate decrease in short term