Chapter 3
Time Value of Money Part 2
 Learning Objectives
 Explain and Illustrate an Annuity
 Determine Future Value of an Annuity
 Determine Present Value of an Annuity
Present Value of Annuity Stream
 Adjust formulas for Annuity Due
 Distinguish between different loan types
 Build an Amortization Schedule
 Calculate Waiting Time and Interest Rates for
an Annuity
Future Value of Stream of
Payments
 Different Amounts at Different Times
 Use FV formula over and over
 Add up each value for Future Value
 Note money can only be “added” at same
point in time
 Is there a short-cut? Sometimes…yes
 Annuity Stream
 Same amount at same interval
Future Value of Multiple Cash Flow
 Same Amount each time and same time interval
between each cash flow
 Shortcut – Annuity Stream Evaluation
 Visualize with time line – page 47
Future Value of Multiple Cash Flow
 Three methods again for finding FV
 Formula or Equation Method
 Calculator Method
 Spreadsheet Method
 Example 3.1 Scholarship for Lisa
 $1,500 annual payment into scholarship fund
 Earns 7% interest over 18 years
 FV is approximately $51,000
Present Value of Annuity Stream
 A similar shortcut for present value
 Three methods but basic same equation
Ordinary Annuity versus Annuity Due
 Need to visualize the difference between
an annuity at the start of the period versus
and annuity at the end of a period
 Start of Period – Annuity Due
 Example rent payment
 End of Period – Ordinary Annuity
 Example car payment
 Original Formulas for Ordinary Annuity
 Adjustment for Annuity Due – multiply by (1+r)
Perpetuities
 Never Ending Annuity Stream
 How can you handle an infinite number of
payments?
 Formula reduces to:
Amortization Schedule
 Typical consumer loans make equal
payments every period
 What is the balance (principal) at the end
of any month if some of the payment is for
interest and some for principal reduction?
 Amortization Schedule shows each
payments application to interest expense
and principal reduction
Three Payment Methods
 All loans contain a repayment of the
original amount (principal) and cost of
borrowed money (interest)
 Types of repayment
 Interest and Principal at Maturity
 Interest as you go, Principal at Maturity
 Interest and Principal as you go
 Why the difference in interest? Table 3.1
Amortization Schedule
 How to build an amortization schedule
 Step One – Determine the payment for each period
given number of periods (n), interest rate (r), and the
present value (PV).
 Step Two – Determine each periods required interest
payment
 Outstanding Balance x Interest rate = Interest expense
 Step Three – Determine principal reduction
 Payment – Interest expense = Principal Reduction
 Step Four – Determine remaining principal
 Beginning of Period Principal – Principal reduction = End of
Period Principal
 Step Five – Repeat Steps Two through Four, n-1
times
Waiting Time
 Same shortcut for Waiting Time, find n with an
annuity stream
Finding Interest Rates with
Annuities
 Interest Rate with Annuities
 Can not isolate interest rate variable
 Must use an iterative process
 Try one interest rate and see if it works…
 Try another interest rate and see if it works…
 Try another interest rate and see if it works…
 Keep going until you find the correct interest rate.
 OR
 Use a calculator or spreadsheet and let it do the
iterative process
Homework
 Problem 9 – Lease versus Buy with TVM
 Problem 15 – Future Value
 Problem 17 – Present Value
 Problem 20 – Payments
 Problem 25 – Amortization Schedule