TIME VALUE OF MONEY REVIEW - Content Time Value of Money SI NG L E AMO U N TS Compound Interest Slides 2 10 Nominal Rate(APR and Periodic Rate Slides 11

TIME VALUE OF MONEY REVIEW - Content Time Value of Money SI...

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Content: Time Value of Money SINGLE AMOUNTS Compound Interest: Slides 2 - 10 Nominal Rate (APR) and Periodic Rate: Slides 11 - 14 Continuous Interest: Slides 15 – 19 ANNUITIES & PERPETUITIES Annuity Problems: Slide 20 Future Value of an (Ordinary) Annuity: Slides 21 – 29 Present Value of an (Ordinary) Annuity: Slides 30 - 33 Amortization Schedules: Slides 34 - 38 EAR: Slides 39 – 47 Annuity Due: Slides 48 – 50 SOLUTIONS TO YOU TRY PROBLEMS: SLIDES 52 - 66 1
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The Future Value Equation: An Amount Under Compound Interest GENERAL EXPRESSION: After n periods, at a periodic interest rate of k, a Present Value ‘PV’ grows to: NOTATION: (1 + k) n is called t he “Future Value Factor for k and n” and is denoted: 2 FV n = PV (1 + k) n FVF k,n = (1 + k) n
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3 The Future Value Factor – Using a Standard Calculator Example: Calculate FVF 12, 10 = (1 + .12) 10 on a standard-calculator. Answer: Standard Calculator Method: 1.12 10 Keys: FVF 12, 10 = 3.105848208 Enter: 1.12 Press: y x Enter: 10 Press: =
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4 Example: A Future Value Problem Example: How much will $1000 be worth if it’s deposited for ten years at a 12% annual interest rate? Solution: FV n = PV (1 + k) n FV 10 = $1000 · (1 + .12) 10 FV 10 = $1000 · 3.105848208 = $ 3,105.85 FVF 12,10 PV n k
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Example: A Future Value Problem PROBLEM 1 ( YOU TRY ): How much will $1000 be worth after 20 periods at a 6% periodic interest rate? SOLUTION: FV n = PV (1 + k) n 5 Check answers to problems Appear at the end of this document.
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6 The Four Generic Time-Value Problems – Compound Interest Problem-Solving: Every time-value problem contains four variables. In the case of single amounts, the four variables are: 1. FV n 2. PV 3. k 4. n Generally, problems will give you three of these four variables , and ask you to find the fourth.
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Example: Unknown Present Value - PV Example: How much do you need to deposit now in order to have $4000 in 10 years at a 12% annual interest rate? Solution: FV n = PV (1 + k) n $4000 = PV (1 + .12) 10 PV = $4000 / (1.12) 10 PV = $4000 / 3.105848208 = $ 1,287.89 7 FV n k
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Example: Unknown Interest Rate, k Problem 2 ( YOU TRY ): What annual interest rate would you need for a $1000 deposit to grow to $4000 in 10 years? Solution ( YOU TRY ): FV n = PV (1 + k) n 8 FV PV n Check answers to problems Appear at the end of this document.
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Example: Unknown Time, n Problem 3 ( YOU TRY ): How many years would it take for a $1000 deposit to grow to $4000 at a 12% annual interest rate? Solution ( YOU TRY ): FV n = PV (1 + k) n 9 Check answers to problems Appear at the end of this document.
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Single Amounts Under Compound Interest – Four Generic Problems 10 GENERIC PROBLEMS: For compound interest involving a single amount, the four generic problems have general solutions. But, it’s probably better just to remember the basic equation and solve it as necessary. TO BE SOLVED FOR: GIVEN: GENERAL SOLUTION: FV n PV, k & n FV n = PV ( 1 + k ) n PV FV n , k & n PV = FV n ( 1 + k ) – n k PV, FV n & n n PV, FV n & k
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Compounding More Frequently Than Once Per Year: Introducing k nom and m Suppose there are m compounding periods per year (e.g. “monthly” ↔ m = 12).
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