SlideShare a Scribd company logo
1 of 34
Download to read offline
Chapter 3: Time
Value of Money (part
2)
A QUICK DOUBLE CHECK
 Calculator set to 4 decimal places
 Calculator set to END (2nd PMT/BGN key)
 Calculator is set to 1 payment/yr (P/Y)
A quick review: a single deposit
   FV = PV (1 + i)n
     What       your money will grow to be
   PV = FV [1/(1 + i)n ]
     What       your future money is worth today
   Inflation adjusted interest rate:
     (1+i)/(1+r)       -1
       Substituting i* for i when controlling for inflation
 What will John’s $100,000 grow to be in
  15 years if he leaves it in an account
  earning an 8% rate of return.
 PV = -100,000
 I/Y = 8
 N = 15
 CPT FV = 317,216.91
Annuities: multiple payments
   Definition -- a series of equal dollar
    payments coming at the end of a certain
    time period for a specified number of time
    periods (n).

   Examples – mortgages, life insurance
    benefits, lottery payments, retirement
    payments.
Compound Annuities
   Definition -- depositing an equal sum of
    money at the end of each time period for a
    certain number of periods and allowing the
    money to grow

   Example – having $50 taken out of each
    paycheck and put in a Christmas account
    earning 9% Annual Percentage Rate.
Future Value of an Annuity
(FVA) Equation
 This equation is used to determine the
  future value of a stream of deposits/
  payments (PMT) invested at a specific
  interest rate (i), for a specific number of
  periods (n)
 For example: the value of your 401(k)
  contributions.
SOLVING FOR FUTURE VALUE
OF AN ANNUITY (MULTIPLE)
 The future value is the unknown
 CPT FV
Calculating the Future Value
(FVA) of an Annuity:
Assuming a $2000 annual contribution
with a 9% rate of return, how much will
an IRA be worth in 30 years?

FVA   = PMT {[(1.09)30 – 1]/.09}
FVA    = $2000 {[13.27 - 1]/.09}
FVA    = $2000 {[12.27]/.09}
FVA     = $2000{136.33}
FVA    = $272,610
Financial Calculator
 PMT = -2000
 I/Y = 9
 N = 30
 CPT FV = 272,615
Solving for Future value:
   Each month, Anna N. deposits her
    paycheck ($5,000) in an account offering a
    monthly interest rate of 6%. How much
    will Anna have in her account at the end of
    1 year?
Financial Calculator
 PMT = -5000
 I/Y = 6
 N = 12
 CPT FV = $84,349.70 at the end of one
  year
Practice Problems
 If Jenny deposits $1,200 each year into a
  savings account earning an Annual Rate
  of return of 2% for 15 years, how much will
  she have at the end of the 15 years?
 How much will she have if she deposits
  $1,200 each month? How much will she
  have if she earns interest monthly?
Yearly
 PMT = -$1,200
 I/Y = 2
 N = 15
 CPT FV= $20,752.10
Extreme Caution!
   Make double sure your time frames are
    consistent……..
     Ifthe payment is a monthly payment; then the
      compounding rate of return has to be a
      monthly rate of return.
     Example: A 15% ANNUAL rate of return is
      equal to a monthly rate of return of 1.25%
     15/12 = 1.25
Monthly
 PMT = $-1,200
 I/Y = .1667 [2/12]
 N = 180     [15*12]
 CPT FV = $251,655.66
Present value (moves backward) &
  Future value (moves forward)
   In real life: Winning
    the lottery (present
    value) or saving for
    retirement (future
    value)
Present Value of an Annuity
(PVA) Equation
   This equation is used to determine the
    present value of a future stream of
    payments, such as your pension fund or
    insurance benefits.
SOLVING FOR PRESENT VALUE
OF AN ANNUITY (MULTIPLE)
 The Present Value is the unknown
 CPT PV
Present Value of an Annuity: An
example: Alimony
What is the present value of 25 annual
payments of $50,000 offered to a soon-to-be
ex-wife, assuming a 5% annual discount rate?
(PVA is the only unknown)

PVA = PMT {[1 – (1/(1.05)25)]/.05}
PVA = $50,000 {[1 – (1/3.38)]/.05}
PVA = $50,000 {[1 – (.295)]/.05}
PVA = $50,000 {[.705]/.05}
PVA = $50,000 {14.10}
PVA = $704,697 lump sum if she takes the
pay off today!
Financial Calculators
 PMT = -50,000
 N = 25
 I/Y = 5
 CPT PV = $704,697.22
Future Value Annuity of that
divorce settlement
   25 annual payments of $50,000 invested
    @ 5% results in
 $2,386,354.94
 A difference of:
     $1,681,354.94
Amortized Loans
   Definition -- loans that are repaid in equal
    periodic installments
   With an amortized loan the interest payment
    declines as your outstanding principal declines;
    therefore, with each payment you will be paying
    an increasing amount towards the principal of
    the loan.
   Examples -- car loans or home mortgages
Solving for the PMT
   No more hypothetical “what ifs”

   You can really use this stuff!
SOLVING FOR PAYMENT
 The Payment is the unknown
 CPT PMT
Buying a Car With 4 Easy Annual
Installments
 What are the annual payments to repay $6,000 at
 15% APR interest? (the payment is the unknown)

 PVA = PMT{[1 – (1/(1.15)4)]/.15}
 $6,000 = PMT {[1 – (.572)]/.15}
 $6,000 = PMT {[.4282/.15]}
 $6,000 = PMT{2.854}
 $6,000/2.854 = PMT
 $2,102.31 = Annual PMT
Financial Calculator
 PV = 6,000
 I/Y = 15
N=4
 CPT PMT = -2,101.59
Buying the same car with monthly
payments
PVA       = PMT{[1 – (1/(1.0125)48)]/.0125}
$6,000 = PMT {[1 – (.55087)]/.0125}
$6,000 = PMT {[.44913/.0125]}
$6,000 = PMT{35.93}
$6,000/{35.93} = PMT
$166.99 = monthly PMT
http://www.bankrate.com
Extreme Caution!
   Make double sure your time frames are
    consistent……..
     Ifthe payment is a monthly payment; then the
      compounding rate of return has to be a
      monthly rate of return.
     Example: A 15% ANNUAL rate of return is
      equal to a monthly rate of return of 1.25%
     15/12 = 1.25
Buying the same car with monthly
payments: Financial Calculator
 PV = 6,000
 I/Y = 1.25 [15/12]
 N = 48     [4*12]
 CPT PMT = $-166.98
Student loan payments
   Guestimate your total
    school loans…..(PVA)
   How many years to
    pay them off? (covert
    to monthly payments)
   At what interest rate?
    R u consolidating?
Review:
    Future value – the value, in the future, of
     a current investment
      Formula?

  Rule of 72 – estimates how long your
   investment will take to double at a given
   rate of return
  Present value – today’s value of an
   investment received in the future
      Formula?
Review (cont’d)
  Annuity – a periodic series of equal
   payments for a specific length of time
  Future value of an annuity – the value, in
   the future, of a current stream of
   investments
      Formula?
    Present value of an annuity – today’s
     value of a stream of investments
     received in the future
      Formula?
Review (cont’d)
   Amortized loans – loans paid in equal
    periodic installments for a specific length
    of time

More Related Content

What's hot

Time Value Of Money Part 1
Time Value Of Money   Part 1Time Value Of Money   Part 1
Time Value Of Money Part 1Alan Anderson
 
Time Value Of Money Part 2
Time Value Of Money   Part 2Time Value Of Money   Part 2
Time Value Of Money Part 2Alan Anderson
 
Chapter 2 introduction to valuation - the time value of money
Chapter 2   introduction to valuation - the time value of moneyChapter 2   introduction to valuation - the time value of money
Chapter 2 introduction to valuation - the time value of moneyKEOVEASNA5
 
Time value of money
Time value of moneyTime value of money
Time value of moneyAnkit Jain
 
Time Value Of Money -Finance
Time Value Of Money -FinanceTime Value Of Money -Finance
Time Value Of Money -FinanceZoha Qureshi
 
GSB711-Lecture-Note-03-The-Time-Value-of-Money
GSB711-Lecture-Note-03-The-Time-Value-of-MoneyGSB711-Lecture-Note-03-The-Time-Value-of-Money
GSB711-Lecture-Note-03-The-Time-Value-of-MoneyUniversity of New England
 
Engineering Economics Introduction
Engineering Economics IntroductionEngineering Economics Introduction
Engineering Economics IntroductionAbinanth Sathya
 
Time value of money- TVM ( Discouting and Compounding)
Time value of money- TVM ( Discouting and Compounding)Time value of money- TVM ( Discouting and Compounding)
Time value of money- TVM ( Discouting and Compounding)Sweetp999
 
Principles of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdf
Principles of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdfPrinciples of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdf
Principles of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdfSonamGulzar
 
Time value of money
Time value of moneyTime value of money
Time value of moneydomsr
 
Time value of money
Time value of moneyTime value of money
Time value of moneyAtif Hossain
 
The investment environment ppt @ bec doms
The investment environment ppt @ bec domsThe investment environment ppt @ bec doms
The investment environment ppt @ bec domsBabasab Patil
 

What's hot (20)

Time Value Of Money Part 1
Time Value Of Money   Part 1Time Value Of Money   Part 1
Time Value Of Money Part 1
 
Time Value of Money
Time Value of MoneyTime Value of Money
Time Value of Money
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
4. time value of money
4. time value of money4. time value of money
4. time value of money
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
Time Value Of Money Part 2
Time Value Of Money   Part 2Time Value Of Money   Part 2
Time Value Of Money Part 2
 
Chapter 2 introduction to valuation - the time value of money
Chapter 2   introduction to valuation - the time value of moneyChapter 2   introduction to valuation - the time value of money
Chapter 2 introduction to valuation - the time value of money
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
Time Value of Money
Time Value of MoneyTime Value of Money
Time Value of Money
 
Time Value of Money
Time Value of MoneyTime Value of Money
Time Value of Money
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
Time Value Of Money -Finance
Time Value Of Money -FinanceTime Value Of Money -Finance
Time Value Of Money -Finance
 
GSB711-Lecture-Note-03-The-Time-Value-of-Money
GSB711-Lecture-Note-03-The-Time-Value-of-MoneyGSB711-Lecture-Note-03-The-Time-Value-of-Money
GSB711-Lecture-Note-03-The-Time-Value-of-Money
 
Engineering Economics Introduction
Engineering Economics IntroductionEngineering Economics Introduction
Engineering Economics Introduction
 
Time value of money- TVM ( Discouting and Compounding)
Time value of money- TVM ( Discouting and Compounding)Time value of money- TVM ( Discouting and Compounding)
Time value of money- TVM ( Discouting and Compounding)
 
chapter 03
chapter 03chapter 03
chapter 03
 
Principles of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdf
Principles of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdfPrinciples of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdf
Principles of Managerial Finance (Lawrence G. Gitman, 13th ED.)-sAyYiEd.pdf
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
The investment environment ppt @ bec doms
The investment environment ppt @ bec domsThe investment environment ppt @ bec doms
The investment environment ppt @ bec doms
 

Viewers also liked

Business Math Chapter 5
Business Math Chapter 5 Business Math Chapter 5
Business Math Chapter 5 Nazrin Nazdri
 
Business Math Chapter 4
Business Math Chapter 4Business Math Chapter 4
Business Math Chapter 4Nazrin Nazdri
 
Introduction to finance
Introduction to financeIntroduction to finance
Introduction to financeNikhil Lohiya
 
7.simple annuities
7.simple annuities7.simple annuities
7.simple annuitieszaragozai
 
Financial management ppt
Financial management pptFinancial management ppt
Financial management pptRanal Nair
 
Credit Basics and Debt Repayment Strategies
Credit Basics and Debt Repayment StrategiesCredit Basics and Debt Repayment Strategies
Credit Basics and Debt Repayment StrategiesBarbara O'Neill
 
Time value of money part 1
Time value of money part 1Time value of money part 1
Time value of money part 1Sudipta Saha
 
Chapter 6: The Time Value of Money
Chapter 6: The Time Value of MoneyChapter 6: The Time Value of Money
Chapter 6: The Time Value of MoneyNada G.Youssef
 
Risk and Return: Portfolio Theory and Assets Pricing Models
Risk and Return: Portfolio Theory and Assets Pricing ModelsRisk and Return: Portfolio Theory and Assets Pricing Models
Risk and Return: Portfolio Theory and Assets Pricing ModelsPANKAJ PANDEY
 
Financial management; loan amortization (4)
Financial management; loan amortization (4)Financial management; loan amortization (4)
Financial management; loan amortization (4)Dr. Amir Ikram
 
portfolio risk
portfolio riskportfolio risk
portfolio riskAttiq Khan
 
Math of ivestment (annuity due and deferred payments)
Math of ivestment (annuity due and deferred payments)Math of ivestment (annuity due and deferred payments)
Math of ivestment (annuity due and deferred payments)Vanessa Joy Mendoza
 

Viewers also liked (20)

Annuity
AnnuityAnnuity
Annuity
 
Annuity Basics
Annuity Basics Annuity Basics
Annuity Basics
 
Annuity
AnnuityAnnuity
Annuity
 
Business Math Chapter 5
Business Math Chapter 5 Business Math Chapter 5
Business Math Chapter 5
 
Business Math Chapter 4
Business Math Chapter 4Business Math Chapter 4
Business Math Chapter 4
 
Introduction to finance
Introduction to financeIntroduction to finance
Introduction to finance
 
Annuity
AnnuityAnnuity
Annuity
 
7.simple annuities
7.simple annuities7.simple annuities
7.simple annuities
 
Financial management
Financial managementFinancial management
Financial management
 
Financial management ppt
Financial management pptFinancial management ppt
Financial management ppt
 
Credit Basics and Debt Repayment Strategies
Credit Basics and Debt Repayment StrategiesCredit Basics and Debt Repayment Strategies
Credit Basics and Debt Repayment Strategies
 
Chapter 6 annuity
Chapter 6 annuityChapter 6 annuity
Chapter 6 annuity
 
Time value of money part 1
Time value of money part 1Time value of money part 1
Time value of money part 1
 
Present value lecture 3
Present value lecture 3Present value lecture 3
Present value lecture 3
 
Risk & Return
Risk & ReturnRisk & Return
Risk & Return
 
Chapter 6: The Time Value of Money
Chapter 6: The Time Value of MoneyChapter 6: The Time Value of Money
Chapter 6: The Time Value of Money
 
Risk and Return: Portfolio Theory and Assets Pricing Models
Risk and Return: Portfolio Theory and Assets Pricing ModelsRisk and Return: Portfolio Theory and Assets Pricing Models
Risk and Return: Portfolio Theory and Assets Pricing Models
 
Financial management; loan amortization (4)
Financial management; loan amortization (4)Financial management; loan amortization (4)
Financial management; loan amortization (4)
 
portfolio risk
portfolio riskportfolio risk
portfolio risk
 
Math of ivestment (annuity due and deferred payments)
Math of ivestment (annuity due and deferred payments)Math of ivestment (annuity due and deferred payments)
Math of ivestment (annuity due and deferred payments)
 

Similar to Understanding the time value of money (annuity)

Similar to Understanding the time value of money (annuity) (20)

Chapter 05 Time Value Of Money
Chapter 05 Time Value Of MoneyChapter 05 Time Value Of Money
Chapter 05 Time Value Of Money
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
Chapter 4.doc
Chapter 4.docChapter 4.doc
Chapter 4.doc
 
Chap005
Chap005Chap005
Chap005
 
Time value Ch6.pdf
Time value Ch6.pdfTime value Ch6.pdf
Time value Ch6.pdf
 
Time Value of Money- managerial finance
Time Value of Money- managerial financeTime Value of Money- managerial finance
Time Value of Money- managerial finance
 
Time value of money2020
Time value of money2020Time value of money2020
Time value of money2020
 
time_value_of_money.ppt
time_value_of_money.ppttime_value_of_money.ppt
time_value_of_money.ppt
 
time_value_of_money.ppt
time_value_of_money.ppttime_value_of_money.ppt
time_value_of_money.ppt
 
Gj11e ch02
Gj11e ch02Gj11e ch02
Gj11e ch02
 
Ross7e ch04
Ross7e ch04Ross7e ch04
Ross7e ch04
 
Chapter 4
Chapter 4Chapter 4
Chapter 4
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
time value of money
time value of moneytime value of money
time value of money
 
Lecture 4 tvm
Lecture 4  tvmLecture 4  tvm
Lecture 4 tvm
 
Cost & Management Accounting 2- TMUC
Cost & Management Accounting 2- TMUCCost & Management Accounting 2- TMUC
Cost & Management Accounting 2- TMUC
 
Chapter 5 Time Value of Money.pptx
Chapter 5 Time Value of Money.pptxChapter 5 Time Value of Money.pptx
Chapter 5 Time Value of Money.pptx
 
Ch06
Ch06Ch06
Ch06
 
Gj11e ch02
Gj11e ch02Gj11e ch02
Gj11e ch02
 
Ff topic 3_time_value_of_money
Ff topic 3_time_value_of_moneyFf topic 3_time_value_of_money
Ff topic 3_time_value_of_money
 

More from DIANN MOORMAN

Labor Market Impact on Women and Men
Labor Market Impact on Women and MenLabor Market Impact on Women and Men
Labor Market Impact on Women and MenDIANN MOORMAN
 
Exploring the Relationship between Financial and Non-financial Risk Taking Be...
Exploring the Relationship between Financial and Non-financial Risk Taking Be...Exploring the Relationship between Financial and Non-financial Risk Taking Be...
Exploring the Relationship between Financial and Non-financial Risk Taking Be...DIANN MOORMAN
 
Techniques for Learning Students' Names
Techniques for Learning Students' NamesTechniques for Learning Students' Names
Techniques for Learning Students' NamesDIANN MOORMAN
 
Learning Styles: How to Teach to a Dog Person if You Must
Learning Styles: How to Teach to a Dog Person if You MustLearning Styles: How to Teach to a Dog Person if You Must
Learning Styles: How to Teach to a Dog Person if You MustDIANN MOORMAN
 
Understanding the Time Value of Money; Single Payment
Understanding the Time Value of Money; Single PaymentUnderstanding the Time Value of Money; Single Payment
Understanding the Time Value of Money; Single PaymentDIANN MOORMAN
 
INTRODUCTION TO FINANCIAL PLANNING
INTRODUCTION TO FINANCIAL PLANNINGINTRODUCTION TO FINANCIAL PLANNING
INTRODUCTION TO FINANCIAL PLANNINGDIANN MOORMAN
 
The Consumer Movement
The Consumer MovementThe Consumer Movement
The Consumer MovementDIANN MOORMAN
 
Consumers in A Changing World
Consumers in A Changing WorldConsumers in A Changing World
Consumers in A Changing WorldDIANN MOORMAN
 
Freshman Learning Community Writing Papers 101
Freshman Learning Community Writing Papers 101Freshman Learning Community Writing Papers 101
Freshman Learning Community Writing Papers 101DIANN MOORMAN
 
How a Bill Becomes a Law
How a Bill Becomes a LawHow a Bill Becomes a Law
How a Bill Becomes a LawDIANN MOORMAN
 
Structure of the Federal Government
Structure of the Federal GovernmentStructure of the Federal Government
Structure of the Federal GovernmentDIANN MOORMAN
 
Freshman Learning Community Challenge
Freshman Learning Community ChallengeFreshman Learning Community Challenge
Freshman Learning Community ChallengeDIANN MOORMAN
 

More from DIANN MOORMAN (12)

Labor Market Impact on Women and Men
Labor Market Impact on Women and MenLabor Market Impact on Women and Men
Labor Market Impact on Women and Men
 
Exploring the Relationship between Financial and Non-financial Risk Taking Be...
Exploring the Relationship between Financial and Non-financial Risk Taking Be...Exploring the Relationship between Financial and Non-financial Risk Taking Be...
Exploring the Relationship between Financial and Non-financial Risk Taking Be...
 
Techniques for Learning Students' Names
Techniques for Learning Students' NamesTechniques for Learning Students' Names
Techniques for Learning Students' Names
 
Learning Styles: How to Teach to a Dog Person if You Must
Learning Styles: How to Teach to a Dog Person if You MustLearning Styles: How to Teach to a Dog Person if You Must
Learning Styles: How to Teach to a Dog Person if You Must
 
Understanding the Time Value of Money; Single Payment
Understanding the Time Value of Money; Single PaymentUnderstanding the Time Value of Money; Single Payment
Understanding the Time Value of Money; Single Payment
 
INTRODUCTION TO FINANCIAL PLANNING
INTRODUCTION TO FINANCIAL PLANNINGINTRODUCTION TO FINANCIAL PLANNING
INTRODUCTION TO FINANCIAL PLANNING
 
The Consumer Movement
The Consumer MovementThe Consumer Movement
The Consumer Movement
 
Consumers in A Changing World
Consumers in A Changing WorldConsumers in A Changing World
Consumers in A Changing World
 
Freshman Learning Community Writing Papers 101
Freshman Learning Community Writing Papers 101Freshman Learning Community Writing Papers 101
Freshman Learning Community Writing Papers 101
 
How a Bill Becomes a Law
How a Bill Becomes a LawHow a Bill Becomes a Law
How a Bill Becomes a Law
 
Structure of the Federal Government
Structure of the Federal GovernmentStructure of the Federal Government
Structure of the Federal Government
 
Freshman Learning Community Challenge
Freshman Learning Community ChallengeFreshman Learning Community Challenge
Freshman Learning Community Challenge
 

Recently uploaded

Hungarys economy made by Robert Miklos
Hungarys economy   made by Robert MiklosHungarys economy   made by Robert Miklos
Hungarys economy made by Robert Miklosbeduinpower135
 
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGeckoRWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGeckoCoinGecko
 
LIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptxLIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptxsonamyadav7097
 
India Economic Survey Complete for the year of 2022 to 2023
India Economic Survey Complete for the year of 2022 to 2023India Economic Survey Complete for the year of 2022 to 2023
India Economic Survey Complete for the year of 2022 to 2023SkillCircle
 
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.KumarJayaraman3
 
ACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTES
ACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTESACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTES
ACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTESKumarJayaraman3
 
The CBR Covered Bond Investor Roundtable 2024
The CBR Covered Bond Investor Roundtable 2024The CBR Covered Bond Investor Roundtable 2024
The CBR Covered Bond Investor Roundtable 2024Neil Day
 
Solution manual for Intermediate Accounting, 11th Edition by David Spiceland...
Solution manual for  Intermediate Accounting, 11th Edition by David Spiceland...Solution manual for  Intermediate Accounting, 11th Edition by David Spiceland...
Solution manual for Intermediate Accounting, 11th Edition by David Spiceland...mwangimwangi222
 
The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?Stephen Perrenod
 
Stock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdfStock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdfMichael Silva
 
Work and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB fundingWork and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB fundingHenry Tapper
 
CLMV-Outlook-March-2024-ENG-20240327.pdf
CLMV-Outlook-March-2024-ENG-20240327.pdfCLMV-Outlook-March-2024-ENG-20240327.pdf
CLMV-Outlook-March-2024-ENG-20240327.pdfSCBEICSCB
 
Contracts with Interdependent Preferences
Contracts with Interdependent PreferencesContracts with Interdependent Preferences
Contracts with Interdependent PreferencesGRAPE
 
Buy and Sell Urban Tots unlisted shares.pptx
Buy and Sell Urban Tots unlisted shares.pptxBuy and Sell Urban Tots unlisted shares.pptx
Buy and Sell Urban Tots unlisted shares.pptxPrecize Formely Leadoff
 
ACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINT
ACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINTACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINT
ACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINTindexPub
 

Recently uploaded (20)

Hungarys economy made by Robert Miklos
Hungarys economy   made by Robert MiklosHungarys economy   made by Robert Miklos
Hungarys economy made by Robert Miklos
 
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGeckoRWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
 
Mobile Money Taxes: Knowledge, Perceptions and Politics: The Case of Ghana
Mobile Money Taxes: Knowledge, Perceptions and Politics: The Case of GhanaMobile Money Taxes: Knowledge, Perceptions and Politics: The Case of Ghana
Mobile Money Taxes: Knowledge, Perceptions and Politics: The Case of Ghana
 
LIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptxLIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptx
 
India Economic Survey Complete for the year of 2022 to 2023
India Economic Survey Complete for the year of 2022 to 2023India Economic Survey Complete for the year of 2022 to 2023
India Economic Survey Complete for the year of 2022 to 2023
 
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
 
ACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTES
ACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTESACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTES
ACCOUNTING FOR BUSINESS.II BRANCH ACCOUNTS NOTES
 
Digital Financial Services Taxation in Africa
Digital Financial Services Taxation in AfricaDigital Financial Services Taxation in Africa
Digital Financial Services Taxation in Africa
 
The CBR Covered Bond Investor Roundtable 2024
The CBR Covered Bond Investor Roundtable 2024The CBR Covered Bond Investor Roundtable 2024
The CBR Covered Bond Investor Roundtable 2024
 
Solution manual for Intermediate Accounting, 11th Edition by David Spiceland...
Solution manual for  Intermediate Accounting, 11th Edition by David Spiceland...Solution manual for  Intermediate Accounting, 11th Edition by David Spiceland...
Solution manual for Intermediate Accounting, 11th Edition by David Spiceland...
 
The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?
 
Stock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdfStock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdf
 
Work and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB fundingWork and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB funding
 
Effects & Policies Of Bank Consolidation
Effects & Policies Of Bank ConsolidationEffects & Policies Of Bank Consolidation
Effects & Policies Of Bank Consolidation
 
Monthly Economic Monitoring of Ukraine No.230, March 2024
Monthly Economic Monitoring of Ukraine No.230, March 2024Monthly Economic Monitoring of Ukraine No.230, March 2024
Monthly Economic Monitoring of Ukraine No.230, March 2024
 
E-levy and Merchant Payment Exemption in Ghana
E-levy and Merchant Payment Exemption in GhanaE-levy and Merchant Payment Exemption in Ghana
E-levy and Merchant Payment Exemption in Ghana
 
CLMV-Outlook-March-2024-ENG-20240327.pdf
CLMV-Outlook-March-2024-ENG-20240327.pdfCLMV-Outlook-March-2024-ENG-20240327.pdf
CLMV-Outlook-March-2024-ENG-20240327.pdf
 
Contracts with Interdependent Preferences
Contracts with Interdependent PreferencesContracts with Interdependent Preferences
Contracts with Interdependent Preferences
 
Buy and Sell Urban Tots unlisted shares.pptx
Buy and Sell Urban Tots unlisted shares.pptxBuy and Sell Urban Tots unlisted shares.pptx
Buy and Sell Urban Tots unlisted shares.pptx
 
ACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINT
ACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINTACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINT
ACADEMIC BANK OF CREDIT: A WORLDWIDE VIEWPOINT
 

Understanding the time value of money (annuity)

  • 1. Chapter 3: Time Value of Money (part 2)
  • 2. A QUICK DOUBLE CHECK  Calculator set to 4 decimal places  Calculator set to END (2nd PMT/BGN key)  Calculator is set to 1 payment/yr (P/Y)
  • 3. A quick review: a single deposit  FV = PV (1 + i)n  What your money will grow to be  PV = FV [1/(1 + i)n ]  What your future money is worth today  Inflation adjusted interest rate:  (1+i)/(1+r) -1  Substituting i* for i when controlling for inflation
  • 4.  What will John’s $100,000 grow to be in 15 years if he leaves it in an account earning an 8% rate of return.  PV = -100,000  I/Y = 8  N = 15  CPT FV = 317,216.91
  • 5. Annuities: multiple payments  Definition -- a series of equal dollar payments coming at the end of a certain time period for a specified number of time periods (n).  Examples – mortgages, life insurance benefits, lottery payments, retirement payments.
  • 6. Compound Annuities  Definition -- depositing an equal sum of money at the end of each time period for a certain number of periods and allowing the money to grow  Example – having $50 taken out of each paycheck and put in a Christmas account earning 9% Annual Percentage Rate.
  • 7. Future Value of an Annuity (FVA) Equation  This equation is used to determine the future value of a stream of deposits/ payments (PMT) invested at a specific interest rate (i), for a specific number of periods (n)  For example: the value of your 401(k) contributions.
  • 8. SOLVING FOR FUTURE VALUE OF AN ANNUITY (MULTIPLE)  The future value is the unknown  CPT FV
  • 9. Calculating the Future Value (FVA) of an Annuity: Assuming a $2000 annual contribution with a 9% rate of return, how much will an IRA be worth in 30 years? FVA = PMT {[(1.09)30 – 1]/.09} FVA = $2000 {[13.27 - 1]/.09} FVA = $2000 {[12.27]/.09} FVA = $2000{136.33} FVA = $272,610
  • 10. Financial Calculator  PMT = -2000  I/Y = 9  N = 30  CPT FV = 272,615
  • 11. Solving for Future value:  Each month, Anna N. deposits her paycheck ($5,000) in an account offering a monthly interest rate of 6%. How much will Anna have in her account at the end of 1 year?
  • 12. Financial Calculator  PMT = -5000  I/Y = 6  N = 12  CPT FV = $84,349.70 at the end of one year
  • 13. Practice Problems  If Jenny deposits $1,200 each year into a savings account earning an Annual Rate of return of 2% for 15 years, how much will she have at the end of the 15 years?  How much will she have if she deposits $1,200 each month? How much will she have if she earns interest monthly?
  • 14. Yearly  PMT = -$1,200  I/Y = 2  N = 15  CPT FV= $20,752.10
  • 15. Extreme Caution!  Make double sure your time frames are consistent……..  Ifthe payment is a monthly payment; then the compounding rate of return has to be a monthly rate of return.  Example: A 15% ANNUAL rate of return is equal to a monthly rate of return of 1.25%  15/12 = 1.25
  • 16. Monthly  PMT = $-1,200  I/Y = .1667 [2/12]  N = 180 [15*12]  CPT FV = $251,655.66
  • 17. Present value (moves backward) & Future value (moves forward)  In real life: Winning the lottery (present value) or saving for retirement (future value)
  • 18. Present Value of an Annuity (PVA) Equation  This equation is used to determine the present value of a future stream of payments, such as your pension fund or insurance benefits.
  • 19. SOLVING FOR PRESENT VALUE OF AN ANNUITY (MULTIPLE)  The Present Value is the unknown  CPT PV
  • 20. Present Value of an Annuity: An example: Alimony What is the present value of 25 annual payments of $50,000 offered to a soon-to-be ex-wife, assuming a 5% annual discount rate? (PVA is the only unknown) PVA = PMT {[1 – (1/(1.05)25)]/.05} PVA = $50,000 {[1 – (1/3.38)]/.05} PVA = $50,000 {[1 – (.295)]/.05} PVA = $50,000 {[.705]/.05} PVA = $50,000 {14.10} PVA = $704,697 lump sum if she takes the pay off today!
  • 21. Financial Calculators  PMT = -50,000  N = 25  I/Y = 5  CPT PV = $704,697.22
  • 22. Future Value Annuity of that divorce settlement  25 annual payments of $50,000 invested @ 5% results in  $2,386,354.94  A difference of:  $1,681,354.94
  • 23. Amortized Loans  Definition -- loans that are repaid in equal periodic installments  With an amortized loan the interest payment declines as your outstanding principal declines; therefore, with each payment you will be paying an increasing amount towards the principal of the loan.  Examples -- car loans or home mortgages
  • 24. Solving for the PMT  No more hypothetical “what ifs”  You can really use this stuff!
  • 25. SOLVING FOR PAYMENT  The Payment is the unknown  CPT PMT
  • 26. Buying a Car With 4 Easy Annual Installments What are the annual payments to repay $6,000 at 15% APR interest? (the payment is the unknown) PVA = PMT{[1 – (1/(1.15)4)]/.15} $6,000 = PMT {[1 – (.572)]/.15} $6,000 = PMT {[.4282/.15]} $6,000 = PMT{2.854} $6,000/2.854 = PMT $2,102.31 = Annual PMT
  • 27. Financial Calculator  PV = 6,000  I/Y = 15 N=4  CPT PMT = -2,101.59
  • 28. Buying the same car with monthly payments PVA = PMT{[1 – (1/(1.0125)48)]/.0125} $6,000 = PMT {[1 – (.55087)]/.0125} $6,000 = PMT {[.44913/.0125]} $6,000 = PMT{35.93} $6,000/{35.93} = PMT $166.99 = monthly PMT http://www.bankrate.com
  • 29. Extreme Caution!  Make double sure your time frames are consistent……..  Ifthe payment is a monthly payment; then the compounding rate of return has to be a monthly rate of return.  Example: A 15% ANNUAL rate of return is equal to a monthly rate of return of 1.25%  15/12 = 1.25
  • 30. Buying the same car with monthly payments: Financial Calculator  PV = 6,000  I/Y = 1.25 [15/12]  N = 48 [4*12]  CPT PMT = $-166.98
  • 31. Student loan payments  Guestimate your total school loans…..(PVA)  How many years to pay them off? (covert to monthly payments)  At what interest rate? R u consolidating?
  • 32. Review:  Future value – the value, in the future, of a current investment  Formula?  Rule of 72 – estimates how long your investment will take to double at a given rate of return  Present value – today’s value of an investment received in the future  Formula?
  • 33. Review (cont’d)  Annuity – a periodic series of equal payments for a specific length of time  Future value of an annuity – the value, in the future, of a current stream of investments  Formula?  Present value of an annuity – today’s value of a stream of investments received in the future  Formula?
  • 34. Review (cont’d)  Amortized loans – loans paid in equal periodic installments for a specific length of time