Midterm Review Class - Notes and Examples[2009]

# Midterm Review Class - Notes and Examples[2009] - Midterm...

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Midterm Review Class : TVM, Bonds, Stocks Future Value: FV = Investment × (1 + r) n Present Value: PV = Future Value (1 + r) n Example 1 (FV): How much can you accumulate in your savings account in 5 years if you deposit \$100 today and the bank pays you a 3% annual interest rate? Example 2 (P V): What is the value today of \$100 to be received at the end of 5 years if the bank pays you a 3% annual interest rate? Example 3 (PV): What is the present value of \$100 to be deposited into a savings account today paying 8% annually, with semi-annual compounding, for two years? A) \$85.48 B) \$100 C) \$116.00 D) \$116.99 Example 4: 0 1 2 3 r = 5% |-----------|-------------|-----------| \$200 \$400 \$300 a) Compute FV at end of year 3 b) Compute PV Example 5: Multiple Cash Flows In two years from today, the following cash flows will have a future value of \$7,651.25: \$500 today, \$Y at the end of one year, and \$5,000 at the end of two years. The annual interest rate is 5%. What is Y? A) \$1,822.44 B) \$1,850.00 C) \$2,000.00 D) \$2,126.25 6ee55a758a6579fe59e3cbe7d07a180784777da2.doc 1

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– Cash flows start at end of first time period – Cash Flows start immediately PV Perpetuity (ordinary) = C r PV Perpetuity due = PV Ordinary Perpetuity x (1 +r) #43 Text (ch.4) Perpetuities: A bank will pay you \$100 per year forever if you deposit \$2500 in the bank today. a) If the first payment is made at the end of the first year, what interest rate is the bank paying? b) Using the interest rate calculated in (a), what is the value of the same perpetuity if the first \$100 payment is made today, instead of at the end of year 1? Basic Annuity Formulas: PV annuity = PVA = C x PVAF (note: C = PMT) where PVAF (r, t) = 1/r – [1/r(1 +r) t ] FV annuity = FVA = C x FVAF (future value annuity factor) where FVAF (r, t) = [(1 + r) t -1] / r Annuity Due: PV (Annuity Due) = PV(Simple Annuity) × (1+r) FV (Annuity Due) = FV (Simple Annuity) × (1+r) # 34 Text (ch.4) You won a lottery payment of \$40 million (nominal) but it actually pays \$2 million per year for 20 years. If the discount rate is 8%, what is the present value of the lottery winnings: a) If the first payment comes at the end of the first year? (ordinary annuity) b) If the first payment comes immediately, what is the PV of the winnings? (annuity due!) c) If the first payment does not come until the end of year 5, what is the PV of the lottery winnings? (delayed annuity!) 6ee55a758a6579fe59e3cbe7d07a180784777da2.doc 2
#41 Text (ch.4): Tricky I now have \$20,000 in the bank earning, earning 0.50% per month. I need \$30,000 to make a down payment on a house. I can save an additional \$100 per month. How long will it take me to accumulate the \$30,000? Growing Annuities and Growing Perpetuities

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## This note was uploaded on 10/04/2011 for the course ADMS 2511 taught by Professor Jiu during the Fall '09 term at York University.

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Midterm Review Class - Notes and Examples[2009] - Midterm...

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