The document discusses interest rates and bond yields. It covers two main theories of how interest rates are determined: the loanable funds theory and liquidity preference theory. The loanable funds theory states that interest rates are determined by the supply and demand of loanable funds in the market. The liquidity preference theory argues that interest rates are determined by the supply of money and demand to hold money. The document also discusses how various economic factors can influence interest rate movements. It defines bond yields and the yield to maturity calculation.
risk and return. Defining Return, Return Example, Defining Risk,Determining Expected Return , How to Determine the Expected Return and Standard Deviation, Determining Standard Deviation (Risk Measure), Portfolio Risk and Expected Return Example, Determining Portfolio Expected Return, Determining Portfolio Standard Deviation, Summary of the Portfolio Return and Risk Calculation, Total Risk = Systematic Risk + Unsystematic Risk,
Liquidity Preference Theory suggests that investors demand higher interest rates or additional premiums for medium or long-term maturities and investments. Simply put, interest rates directly indicate the price of the money.
https://efinancemanagement.com/investment-decisions/liquidity-preference-theory
What is interest ? Types of interest & Rate of interest
various theory of interest
1) Classical theory
2) Loanable fund theory
their criticism and explaination
risk and return. Defining Return, Return Example, Defining Risk,Determining Expected Return , How to Determine the Expected Return and Standard Deviation, Determining Standard Deviation (Risk Measure), Portfolio Risk and Expected Return Example, Determining Portfolio Expected Return, Determining Portfolio Standard Deviation, Summary of the Portfolio Return and Risk Calculation, Total Risk = Systematic Risk + Unsystematic Risk,
Liquidity Preference Theory suggests that investors demand higher interest rates or additional premiums for medium or long-term maturities and investments. Simply put, interest rates directly indicate the price of the money.
https://efinancemanagement.com/investment-decisions/liquidity-preference-theory
What is interest ? Types of interest & Rate of interest
various theory of interest
1) Classical theory
2) Loanable fund theory
their criticism and explaination
Assignment for my macroeconomics class covering fiancial markets, financial intermediaries & institutions, the federal government deficit as well as time value money concepts.
Week- 5 Interest Rates and Stock MarketMoney and Banking Econ .docxalanfhall8953
Week- 5 Interest Rates and Stock Market
Money and Banking Econ 311
Thursday 7 - 9:45
Instructor: Thomas L. Thomas
Response over Time to an Increase in Money Supply Growth
2
Risk Structure of Interest Rates
Bonds with the same maturity have different interest rates due to:
Default risk
Liquidity
Tax considerations
Long-Term Bond Yields, 1919–2011
Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve; www.federalreserve.gov/releases/h15/data.htm.
4
Risk Structure of Interest Rates (cont’d)
Default risk: probability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value
U.S. Treasury bonds are considered default free (government can raise taxes).
Risk premium: the spread between the interest rates on bonds with default risk and the interest rates on (same maturity) Treasury bonds
5
Bond Ratings by Moody’s, Standard and Poor’s, and Fitch
6
Risk Structure of Interest Rates (cont’d)
Liquidity: the relative ease with which an asset can be converted into cash
Cost of selling a bond
Number of buyers/sellers in a bond market
Income tax considerations
Interest payments on municipal bonds are exempt from federal income taxes.
Term Structure of Interest Rates
Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different
Yield curve: a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations
Upward-sloping: long-term rates are above
short-term rates
Flat: short- and long-term rates are the same
Inverted: long-term rates are below short-term rates
Facts that the Theory of the Term Structure of Interest Rates Must Explain
Interest rates on bonds of different maturities move together over time
When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term rates are high, yield curves are more likely to slope downward and be inverted
Yield curves almost always slope upward
9
Three Theories to Explain the Three Facts
Expectations theory explains the first two facts but not the third
Segmented markets theory explains fact three but not the first two
Liquidity premium theory combines the two theories to explain all three facts
10
Expectations Theory
The interest rate on a long-term bond will equal an average of the short-term interest rates that people expect to occur over the life of the long-term bond
Buyers of bonds do not prefer bonds of one maturity over another; they will not hold
any quantity of a bond if its expected return
is less than that of another bond with a different maturity
Bond holders consider bonds with different maturities to be perfect substitutes
11
Expectations Theory: Example
Let the c.
Question 1Response 1Development inside and out effects t.docxaudeleypearl
Question 1:
Response 1:
Development inside and out effects the entire country's economy. It impacts the managing body, regardless the clearly irrelevant subtleties in the average person's dependably life. Both a conditions and clear deferred results of how the economy is getting along, swelling has the two its fans and spoilers. Distinctive envisions that particular degrees of swelling are helpful for a prospering economy, yet that progressively critical rates raise concerns. It can degrade the money basically and, at logically lamentable, has been a key part to subsidences.
Swelling, as referenced, is the rate a worth ascensions, and fundamentally how much the dollar is worth at a given moment concerning checking. The idea behind swelling being an impact for good in the economy is that a reasonable enough rate can nudge financial movement without debasing the money so much that it ends up being basically vain (Kohn, 2006).
Swelling can in like manner falter from asset for asset. Subordinate upon the season, the expense of gas could go up independently from with everything considered headway as it routinely does as summer moves close. In reality, there is even a term - focus improvement - for swelling that parts in everything except for sustenance and imperativeness (gas and oil), as these regions have separate factors that add to them. There are a wide degree of sorts of swelling, subordinate upon what remarkable is being viewed comparatively as what the development rate truly is by all accounts. For example, what happens if the swelling rate is well over the Fed's normal goal? At a higher rate, yet still in the single digits, that is known as walking swelling. It is seen as concerning yet sensible (Ball, 2006).
Swelling is generally depicted reliant on its rate and causes. By and large, Inflation happens in an economy when vitality for thing and experiences outmaneuvers the supply of yield. in this manner, clarifications behind Inflation have different sides, the intrigue side and supply side. The widely inclusive activity of hazard premiums in driving enlargement pay over the scope of advancing years is dependable with secured budgetary improvement and inside and out oblige cash related procedure events in the moved economies. The degree for further fitting budgetary enabling seen with money related stars seems to have declined amidst the enough low advance charges and gigantic monetary records of national banks (Bodie, 2016).
In relentless time, the correspondence of perils has wound up being constantly phenomenal, the general point of view has lit up, and money related conditions have engaged on net. With the work superstar proceeding to reinforce, and GDP improvement expected to keep up a vital good ways from back in the consequent quarter, it likely will be fitting soon to change the affiliation supports rate. Likewise, if the economy propels as shown by the SEP concentrate way, the affiliation supports rate will probably app ...
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2. The Theory of Interest Rate
Loan-able Funds Theory
Liquidity Preference Theory
Forces that affect Interest Rates
Interest Rate Fundamentals
Structure of Interest Rates
Time Value of Money and Interest Rates
2
3. An interest rate is the price paid by a borrower (or debtor) to
a lender (or creditor) for the use of resources during some
time interval. The amount of the loan is the principal, and
the price paid is typically expressed as a percentage of the
principal per unit of time (generally a year).
Interest rates are among the most closely watched variables
in the economy. Thus, participants in financial markets
attempt to anticipate interest rate movements when
restructuring their positions so that they can capitalize on
favorable movements or reduce their institution’s exposure to
unfavorable movements.
3
4. There are two theories of the determination of the interest rate
A. Loanable funds theory and
B. Liquidity preference theory.
4
5. Theory of how the general level of interest
rates are determined
Explains how economic and other factors
influence interest rate changes
Interest rates determined by demand and
supply for loanable funds
5
6. This theory proposes that the general level of
interest rates is determined by the complex
interaction of two forces.
The first is the total demand for funds by firms,
governments, and households (or individuals),
which carry out a variety of economic activities
with those funds. This demand is negatively
related to the interest rate (except for the
government’s demand, which may frequently not
depend on the level of the interest rate).
6
7. The second force affecting the level of the
interest rate is the total supply of funds by firms,
governments, banks and individuals. Supply is
positively related to the level of interest rates, if
all other economic factors remain the same. With
rising rates, firms and individuals save and lend
more, and banks are more eager to extend more
loans. (A rising interest rate probably does not
significantly affect the government’s supply of
savings).
7
8. Equilibrium in the Market
The equilibrium interest rate is the rate that equates
the aggregate demand for loanable funds with
aggregate supply of loanable funds.
The aggregate demand for funds (DA) can be written as:
DA = Dh + Db + Dg + Df
where Dh = household demand for loanable funds
Db = business demand for loanable funds
Dg = government demand for loanable funds
Df = foreign demand for loanable funds
8
9. The aggregate supply for funds (SA) can be written as:
SA = Sh + Sb + Sg + Sf
where Sh = household supply for loanable funds
Sb = business supply for loanable funds
Sg = government supply for loanable funds
Sf = foreign supply for loanable funds
9
11. The Results of a Shift in the Demand for Savings
If aggregate demand for loanable funds increases without aggregate
increase in aggregate supply, there will be a shortage of loanable
funds and interest rate will rise until an additional supply of
loanable funds is available to accommodate excess demand.
11
12. The Results of a Shift in the Supply of Savings:
Conversely, an increase in aggregate supply of loanable funds without a
corresponding increase in aggregate demand will result in a surplus of
loanable funds. In this case interest rate will fall until the quantity of
funds supplied no longer exceeds the quantity of funds demanded.
12
13. In many cases, both supply and demand for
loanable funds are changing over time.
Given an initial equilibrium situation, the
equilibrium interest rate should rise when
DA > SA and fall when DA < SA
13
14. The Liquidity Preference theory, originally
developed by John Maynard Keynes, analyzes
the equilibrium level of the interest rate
through the interaction of the supply of money
and the public’s aggregate demand for holding
money. Keynes assumed that most people hold
wealth in only two forms: “money” and
“bonds”.
14
15. For Keynes, money is equivalent to currency
and demand deposits, which pay little or no
interest but are liquid and may be used for
intermediate transactions. Bonds represent a
broad Keynesian category and include long-
term, interest-paying financial assets that are
not liquid and that pose some risk because
their prices vary inversely with the interest
rate level. Bonds may be liabilities of
governments or firms.
15
17. The real rate is the growth in the power to consume
over the life of a loan. The nominal rate of interest, by
contrast, is the number of monetary units to be paid
per unit borrowed and is, in fact, the observable
market rate on a loan. In the absence of inflation, the
nominal rate equals the real rate. The relationship
between inflation (Inflation is a state of disequilibrium
at which aggregate demand exceeds aggregate supply
at the existing prices causing a rise in general price
level) and interest rates is the well-known Fisher’s Law,
which can be expressed this way:
17
18. (1+ i) = (1+ r) X (1+ p)
Where, i = the nominal rate,
r = the real rate,
p= the expected percentage change in the price
level of goods and services over the loan’s life.
The above equation is approximately close enough:
i = r+ p
When the real interest rate is low, there are
greater incentives to borrow and fewer incentives
to lend.
18
19. Interest rate movements affect the values of virtually
all securities
They have a direct influence on debt instruments
- Bonds, Securities
They have an indirect influence on stocks and
exchange rates
Interest rates changes impact the value of financial
institutions
Managers of financial institutions closely monitor
rates
Interest rate risk is a major risk impacting financial
institutions
Changes in interest rates impact the real economy
19
21. Economic Growth:
Expected impact is an outward shift in the
demand schedule without obvious shift in supply
Result is an increase in the equilibrium interest
rate
21
22. Inflation
If inflation is expected to increase
Households may reduce their savings to make
purchases before prices rise
Supply shifts to the left, raising the equilibrium rate
Also, households and businesses may borrow more to
purchase goods before prices increase
Demand shifts outward, raising the equilibrium rate
22
23. Money Supply
When the central bank increases the money
supply, it increases supply of loanable funds
Places downward pressure on interest rates
23
24. Budget Deficit
Increase in deficit increases the quantity of
loanable funds demanded
Demand schedule shifts outward, raising rates
Government is willing to pay whatever is
necessary to borrow funds, “crowding out” the
private sector
24
25. Foreign Flows
In recent years there has been massive flows between
countries
Driven by large institutional investors seeking high returns
They invest where interest rates are high and currencies are
not expected to weaken
These flows affect the supply of funds available in each
country
Investors seek the highest real after-tax, exchange rate
adjusted rate of return around the world
25
26. Change in the money supply has three different
effects upon the level of the interest rate
the liquidity effect,
the income effect, and
the price expectations effect.
26
27. i. Liquidity Effect: This effect represents the initial reaction of
the interest rate to a change in the money supply. With an
increase in the money supply, the initial reaction should be a
fall in the rate. The reason for the fall is that a rise in the
money supply represents a shift in the supply curve.
Figure: The Liquidity Effect of an Increase in the Money Supply
27
28. ii. Income Effect: A decline in the supply would tend to cause
a contraction. An increase in the money is economically
expansionary; more loans are available and extended, more
people are hired or work longer, and consumers and
producers purchase more goods and services. Thus, money
supply changes can cause income in the system to vary.
Figure: The Income Effect of a Change in the Money Supply
28
29. iii. Price Expectations Effect:
Although an increase in the money supply is an economically
expansionary policy, the resultant increase in income depends
substantially on the amount of slack in the economy at the
time of the Central Bank’s action.
-If the economy is operating at less than full strength, an
increase in the money supply can stimulate production,
employment, and output;
-if the economy is producing all or almost all of the goods and
services it can (given the size of the population and the
amount of capital goods), then an increase in the money
supply will largely stimulate expectations of a rising level of
prices for goods and services.
Thus, the price expectations effect usually occurs only if the
money supply grows in a time of high output.
29
30. 1. Features of a Bond:
Maturity
Principal Value
Coupon Rate
30
31. 2. Yield on a Bond:
The yield on a bond investment should reflect
the coupon interest that will be earned plus
either (1) any capital gain that will be realized
from holding the bond to maturity, or (2) any
capital loss that will be realized from holding
the bond to maturity.
31
32. The yield to maturity is a formal, widely accepted
measure of the rate of return on a bond. The yield
to maturity of a bond takes into account the
coupon interest and any capital gain or loss, if the
bond were to be held to maturity. The yield to
maturity is defined as the interest rate that makes
the present value of the cash flow of a bond equal
to the bond’s market price. In mathematical
notation, the yield to maturity, y, is found by
solving the following equation for y.
32
33. Where, P = market price of bond
C = coupon interest
n = time to maturity
)1(
.........
)1()1()1( y
c
Y
c
y
c
Y
c
p
33
34. The yield to maturity is determined by a trial-error process. The
steps in that process are as follows:
Step-1: Select an interest rate.
Step-2: Compute the present value of each cash flow using the
interest rate selected in step-1.
Step-3: Total the present value of the cash flows found in step-2.
Step-4: Compare the total present value found in step-3 with the
market price of the bond and, if the total present value of the
cash flows found in step-3 is:
34
35. Equal to the market price, then the interest rate
used in step-1 is the yield to maturity;
Greater than the market price, then the interest rate
is not the yield to maturity. Therefore, go back to
step-1 and use a higher interest rate.
Less than the market price, the interest rate is not
the yield to maturity. Therefore, go back to step-1
and use a lower interest rate.
35
36. 3. The Base Interest Rate:
The securities issued by the government of the
country, popularly referred to as Treasury Securities
or simply Treasuries, are backed by the full faith and
credit of the government. Consequently, market
participants throughout the world view them as
having no credit risk. As a result, historically the
interest rates on Treasury Securities have served as
the benchmark, interest rates throughout the
domestic economy, as well as in international capital
markets.
36
37. 4. The Risk Premium:
Market participants’ talk of interest rates on non-
Treasury securities as “trading at a spread” to a
particular on-the- run Treasury security (or a spread
to any particular benchmark interest rate selected).
37
38. We can express the interest rate offered on a non-Treasury
security as: For example, if the yield on a 10-year non-Treasury
security is 7% and the yield on a 10-year Treasury security is 6%,
the spread is 100 basis points. This spread reflects the
additional risks the investor faces by acquiring a security that is
not issued by the government and, therefore
Base interest rate + Spread Or, equivalently,
Base interest rate + Risk Premium
One of the factors affecting interest rate is the expected rate
of inflation. That is, the base interest rate can be expressed as:
Base interest rate = Real rate of interest + Expected rate of
inflation
38
39. 5. Types of Issues
6. Perceived Creditworthiness of Issuer
39
40. 7. Term to Maturity
The volatility of a bond’s price is dependent on its
maturity. More specifically, with all other factors
constant , the longer the maturity of a bond, the
greater the price volatility resulting from a change in
market yields. The spread between any two maturity
sectors of the market is called a maturity spread or
yield curve spread. The relationship between the
yields on comparable securities but different maturities
is called the term structure of interest rates.
40
41. 8. Inclusion of Options:
An option that is included in a bond issue is
referred to as an option.
call provision
put provision
convertible bond
41
42. 9. Taxability of Interest:
The yield on a taxable bond issue after income taxes are paid
is equal to:
After-tax yield = Pretax yield (1- Marginal Tax Rate)
Alternatively, we can determine the yield that must be
offered on a taxable bond issue to give the same after-tax
yield as a tax-exempt issue. This yield is called the
equivalent taxable yield and is determined as follows:
ratetaxmarginal-1
yieldexempt-Tax
YieldTaxableEquivalent
42
43. Time Value of Money (TVM) means changes of value
of time over time. Over the time, value of the
money changes and so, same amount of money at
current time and in some future time is not
considered as equally worthy – this is called the
theory of time preference.
43
44. TVM is determined by a number of factors such as:
Consumption preference – people prefer current consumption
to future consumption of same level of satisfaction.
Uncertainty – Future is always uncertain. People would like to
be compensated for that uncertain future cash flow against
certain current cash flow.
Inflation – The purchasing power of money is always depleting,
as inflation is a common factor for any economy. Therefore,
more cash flow is required to purchase same consumption worth
as some current level of cash flow can do.
Investment Opportunity – capital itself has its return. In a
capital market, one is expected to get some return at market
rate called “pure interest rate”. Therefore, whatever may be
the cash flow now; the future cash flow should be more than
this.
44
45. Congratulations!!! You have won a cash prize! You
have two payment options: A - Receive $10,000 now
or B - Receive $10,000 in three years. Which option
would you choose?
45
46. If you're like most people, you would choose to
receive the $10,000 now. After all, three years is
a long time to wait. Why would any rational
person defer payment into the future when he or
she could have the same amount of money now?
For most of us, taking the money in the present
is just plain instinctive. So at the most basic
level, the time value of money demonstrates
that, all things being equal, it is better to have
money now rather than later.
46
47. But why is this? A $100 bill has the same value as a
$100 bill one year from now, doesn't it? Actually,
although the bill is the same, you can do much more
with the money if you have it now because over time
you can earn more interest on your money.
Back to our example: by receiving $10,000 today, you
are poised to increase the future value of your money
by investing and gaining interest over a period of
time. For Option B, you don't have time on your side,
and the payment received in three years would be
your future value. To illustrate, we have provided a
timeline:
47
48. If you are choosing Option A, your future value will
be $10,000 plus any interest acquired over the three
years. The future value for Option B, on the other
hand, would only be $10,000. So how can you
calculate exactly how much more Option A is worth,
compared to Option B? Let's take a look.
48
49. If you choose Option A and invest the total amount at
a simple annual rate of 4.5%, the future value of your
investment at the end of the first year is $10,450,
which of course is calculated by multiplying the
principal amount of $10,000 by the interest rate of
4.5% and then adding the interest gained to the
principal amount:
Future value of investment at end of first year:
=($10,000x0.045)+$10,000
= $10,450
49
50. You can also calculate the total amount of a one-year
investment with a simple manipulation of the above
equation:
Original equation: ($10,000 x 0.045) + $10,000 = $10,450
Manipulation: $10,000 x [(1 x 0.045) + 1] = $10,450
Final equation: $10,000 x (0.045 + 1) = $10,450
50
51. The manipulated equation above is simply a removal of
the like-variable $10,000 (the principal amount) by
dividing the entire original equation by $10,000.
If the $10,450 left in your investment account at the end
of the first year is left untouched and you invested it at
4.5% for another year, how much would you have? To
calculate this, you would take the $10,450 and multiply
it again by 1.045 (0.045 +1). At the end of two years, you
would have $10,920:
Future value of investment at end of second year:
=$10,450x(1+0.045)
= $10,920.25
51
52. The above calculation, then, is equivalent to the following
equation:
Future Value = $10,000 x (1+0.045) x (1+0.045)
Think back to math class and the rule of exponents, which
states that the multiplication of like terms is equivalent to
adding their exponents. In the above equation, the two like
terms are (1+0.045), and the exponent on each is equal to
1. Therefore, the equation can be represented as the
following:
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53. We can see that the exponent is equal to the number of
years for which the money is earning interest in an
investment. So, the equation for calculating the three-year
future value of the investment would look like this:
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54. This calculation shows us that we don't need to calculate
the future value after the first year, then the second year,
then the third year, and so on. If you know how many years
you would like to hold a present amount of money in an
investment, the future value of that amount is calculated by
the following equation:
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55. If you received $10,000 today, the present value would of
course be $10,000 because present value is what your
investment gives you now if you were to spend it today. If
$10,000 were to be received in a year, the present value of
the amount would not be $10,000 because you do not have
it in your hand now, in the present. To find the present
value of the $10,000 you will receive in the future, you
need to pretend that the $10,000 is the total future value of
an amount that you invested today. In other words, to find
the present value of the future $10,000, we need to find out
how much we would have to invest today in order to receive
that $10,000 in the future.
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56. To calculate present value, or the amount that we would
have to invest today, you must subtract the (hypothetical)
accumulated interest from the $10,000. To achieve this, we
can discount the future payment amount ($10,000) by the
interest rate for the period. In essence, all you are doing is
rearranging the future value equation above so that you may
solve for P. The above future value equation can be rewritten
by replacing the P variable with present value (PV) and
manipulated as follows:
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57. Let's walk backwards from the $10,000 offered in Option B.
Remember, the $10,000 to be received in three years is
really the same as the future value of an investment. If
today we were at the two-year mark, we would discount the
payment back one year. At the two-year mark, the present
value of the $10,000 to be received in one year is
represented as the following:
Present value of future payment of $10,000 at end of year
two:
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58. Note that if today we were at the one-year mark, the above
$9,569.38 would be considered the future value of our
investment one year from now.
Continuing on, at the end of the first year we would be
expecting to receive the payment of $10,000 in two years. At
an interest rate of 4.5%, the calculation for the present
value of a $10,000 payment expected in two years would be
the following:
Present value of $10,000 in one year:
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59. Of course, because of the rule of exponents, we don't have
to calculate the future value of the investment every year
counting back from the $10,000 investment at the third year.
We could put the equation more concisely and use the
$10,000 as FV. So, here is how you can calculate today's
present value of the $10,000 expected from a three-year
investment earning 4.5%:
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60. So the present value of a future payment of $10,000 is
worth $8,762.97 today if interest rates are 4.5% per
year. In other words, choosing Option B is like taking
$8,762.97 now and then investing it for three years.
The equations above illustrate that Option A is better
not only because it offers you money right now but
because it offers you $1,237.03 ($10,000 - $8,762.97)
more in cash! Furthermore, if you invest the $10,000
that you receive from Option A, your choice gives you a
future value that is $1,411.66 ($11,411.66 - $10,000)
greater than the future value of Option B.
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61. Let's add a little spice to our investment knowledge.
What if the payment in three years is more than the
amount you'd receive today? Say you could receive either
$15,000 today or $18,000 in four years. Which would you
choose? The decision is now more difficult. If you choose
to receive $15,000 today and invest the entire amount,
you may actually end up with an amount of cash in four
years that is less than $18,000. You could find the future
value of $15,000, but since we are always living in the
present, let's find the present value of $18,000 if interest
rates are currently 4%. Remember that the equation for
present value is the following:
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62. In the equation above, all we are doing is discounting
the future value of an investment. Using the numbers
above, the present value of an $18,000 payment in four
years would be calculated as the following:
Present Value
From the above calculation we now know our choice is
between receiving $15,000 or $15,386.48 today. Of
course we should choose to postpone payment for four
years!
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63. These calculations demonstrate that time literally is
money - the value of the money you have now is not
the same as it will be in the future and vice versa. So,
it is important to know how to calculate the time value
of money so that you can distinguish between the
worth of investments that offer you returns at different
times.
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