Chap3_2009

# Chap3_2009 - Chapter 3 The Time Value of Money Learning...

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Chapter 3 The Time Value of Money

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Learning Objectives After studying Chapter 3, you should be able to: 1. Understand what is meant by "the time value of money." 2. Understand the relationship between present and future value. 3. Describe how the interest rate can be used to adjust the value of cash flows – both forward and backward – to a single point in time. 4. Calculate both the future and present value of: (a) an amount invested today; (b) a stream of equal cash flows (an annuity); and (c) a stream of mixed cash flows. 5. Distinguish between an “ordinary annuity” and an “annuity due.” 6. Use interest factor tables and understand how they provide a shortcut to calculating present and future values. 7. Use interest factor tables to find an unknown interest rate or growth rate when the number of time periods and future and present values are known. 8. Build an “amortization schedule” for an installment-style loan.
Topics The Interest Rate Simple Interest Compound Interest Amortizing a Loan Compounding More Than Once per Year

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Obviously, \$10,000 today . You already recognize that there is TIME VALUE TO MONEY !! The Interest Rate Which would you prefer -- \$10,000 today or \$10,000 in 5 years ?
TIME allows you the opportunity to postpone consumption and earn INTEREST . Why TIME? Why is TIME such an important element in your decision?

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Types of Interest • Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). Simple Interest Interest paid (earned) on only the original amount, or principal, borrowed (lent).
Simple Interest Formula Formula SI = P 0 ( i )( n ) SI : Simple Interest P 0 : Deposit today (t=0) i : Interest Rate per Period n : Number of Time Periods

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• SI = P 0 ( i )( n ) = \$1,000 ( .07 )( 2 ) = \$140 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?
FV = P 0 + 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 (FV) • What is the Future Value ( FV ) of the deposit?

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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. Simple Interest (PV) • What is the Present Value ( PV ) of the previous problem?
5000 10000 15000 20000 1st Year 10th Year 20th Year 30th Year Future Value of a Single \$1,000 Deposit 10% Simple Interest 7% Compound Interest 10% Compound Interest Why Compound Interest? Future Value (U.S. Dollars)

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## This note was uploaded on 07/06/2009 for the course BUS BAM314 taught by Professor Na during the Spring '09 term at 東京大学.

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Chap3_2009 - Chapter 3 The Time Value of Money Learning...

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