ADMS 3530 Review Session - Notes and Examples Ch.4: TVM PV & FV: SINGLE CASH FLOWS Future Value: FV = PV × (1 + r)n

Present Value: PV = Future Value (1 + r)n PV & FV: MULTIPLE CASH FLOWS Example 1: Multiple Cash Flows In two years from today, the following cash flows will have a future value of $3032.32: $200 today, $Y at the end of one year, and $2,400 at the end of two years. The annual interest rate is 4%. What is Y? A) $330.00 B) $400.00 C) $416.00 D) $432.64 E) $167.55 PERPETUITIES & ANNUITIES Ordinary (regular) Annuity & Ordinary Perpetuity – Cash flows start at end of first time period Perpetuity Due & Annuity Due – Cash Flows start immediately PV Perpetuity (ordinary) = C r PV Perpetuity due = PV Ordinary Perpetuity x (1 +r) Basic Annuity Formulas: PVannuity = PVA = C x PVAF (note: C = PMT) FV annuity = FVA = C x FVAF (future value annuity factor) Annuity Due: PV (Annuity Due) = PV(Simple Annuity) × (1+r) FV (Annuity Due) = FV (Simple Annuity) × (1+r)

3530_Final_Tutorial_-_Notes_and_Problems Updated.docx

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Example 2: Delayed Annuity What is the present value of a four-year annuity of $100 per year that begins two years from today if the discount rate is 9 percent? A) B) C) D) E) $297.22 $323.86 $356.85 $388.97 $451.64

EFFECTIVE ANNUAL INTEREST RATES (EAR) – see Lecture 3 (TVM) Notes Two Options: EAR = Compounded rate EAR = (1 + im)m -1 APR = Finding nominal rate using simple interest APR = im x m Note: EAR = APR with annual compounding EAR > APR when interest in calculated more than once/yr Example 3: EAR You are expected to pay $1,883.33 per month on a one-year loan with a principal of $20,000. What is the EAR of this loan? A) 13.00% B) 13.80% C) 23.19% D) 25.82% E) 16.55% Example 4: Mortgages: You want to buy a house that costs $400,000. You make a 20% down payment and finance the rest with a 25 year mortgage. The mortgage has a five year