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# 468-2 - Chapter 2 INTEREST RATES Nominal Interest Rates...

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Chapter 2 - INTEREST RATES Nominal Interest Rates: Interest rates observed in financial markets, e.g., ___________________________________. REVIEW OF TIME VALUE OF MONEY Compound interest, based on reinvestment assumption. Compounded because interest is paid in current period on interest earned in previous periods, "interest on interest." Simple interest: Interest not reinvested. See Figure 2-2 on p. 30. Formulas for compound interest for LUMP SUMS: FV = PV (1 + i ) n "compounding," FV of a lump sum today (PV) PV = FV / (1 + i ) n "discounting," PV of a future lump sum (FV) Examples of LUMP SUM: \$1000 lump sum invested for two years @ 12%: FV = \$1000 x (1.12) 2 = \$1254.40 PV of a lump sum of \$10,000 to be received in 6 years @ 8%? PV = \$10,000 / (1.08) 6 = \$6,301.70 @ 12%: \$10,000 / (1.12) 6 = \$5,066.31 @ 16%: \$10,000 / (1.16) 6 = \$4,104.42 @ 16%, semi-annual compounding: \$10,000 / (1.08) 12 = \$3971.14 (8% per semi-annual period for 12 semi-annual periods) Notice: As interest rates increase (decrease), PV (price) decreases (increases). Logic : a) At a higher interest rate, fewer funds have to be invested today to grow to \$10,000 in 6 years. b) The higher your required rate of return, the less you are willing to pay today for a fixed CF later. c) The riskier the investment, the higher the discount rate (int rate) and the lower the price. BUS 468 / MGT 568: FINANCIAL MARKETS – CH 2 Professor Mark J. Perry 1

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Examples of FV of a LUMP SUM: \$10,000 lump sum invested for 6 years, solve for FV: @ 8%: \$10,000 x (1.08) 6 = \$15,868.74 @12%: \$10,000 x (1.12) 6 = \$19,738.23 @16%: \$10,000 x (1.16) 6 = \$24,363.96 @16% semi-annual compounding: \$10,000 x (1.08) 12 = \$25,181.70 Examples of PV of an ANNUITY: \$10,000 annual PMT for 6 years, solve for PV N I PV* PMT FV 6 8% (\$46,228.80) \$10,000 0 If you receive \$10,000 per quarter for 6 years at 8% annual rate: N I PV* PMT FV 24 2% (\$189,139) \$10,000 0 If PMTs are paid at the BEGINNING of the quarter: Set calculator: ORANGE KEY, BEG/END, Solve for PV. N I PV* PMT FV 24 2% (\$192,922) \$10,000 0 or leave at END of period and solve for N = 23 + \$10,000 \$182,922 (23 future CFs) + \$10,000 today = \$192,922 Examples of FV of an Annuity Invest \$10,000 each year for 6 years, solve for FV @ 8% N I PV PMT FV* 6 8% 0 \$10,000 \$73,359 Invest \$10,000 each quarter for 6 years @ 8% BUS 468 / MGT 568: FINANCIAL MARKETS – CH 2 Professor Mark J. Perry 2
N I PV PMT FV* 24 2% 0 \$10,000 \$304,218 If investments take place at the BEGINNING of the quarter: Set calculator: ORANGE KEY, BEG/END, Solve for FV. N I PV PMT FV* 24 2% 0 \$10,000 \$310,303 Solving for Effective Annual Return The frequency of payments/CFs affects the true annual rate, called the Effective Annual Return (EAR). Rule: the more frequent the payments, the higher the EAR. Formula: EAR = ( 1 + i/m ) m - 1, where m is the number of compounding periods in the year. Examples using 12% interest rate: Compounding Periods: Annual: 1.12 - 1 = .12 or 12% Semi-Annual: (1.06) 2 - 1 = .1236 or 12.36% Quarterly: (1.03) 4 - 1 = .1255 or 12.55% Monthly: (1.01) 12 - 1 = .126825 or 12.6825% Daily (360): (1.000333) 360 - 1 = .1274743 or 12.74743% Daily (365): (1.000333) 365 - 1 = .1274745 or 12.74746% Continuous: (.12) e x - 1 = .127497 or 12.7497% HP Calculator: Put the annual interest rate in I/YR Put the number of compounding periods in PMT key, (ORANGE Key, P/YR) Solve for the EFF% Example for 12% interest, monthly compounding: 12, I/YR 12, ORANGE KEY, PMT ORANGE KEY, EFF% Mortgage Points and Solving for the APR (Annual Percentage Rate): BUS 468 / MGT 568: FINANCIAL MARKETS – CH 2 Professor Mark J. Perry 3

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\$100,000, 30 year mortgage @ 6%, 2 points (2%): Solve for monthly PMT: N I PV PMT* FV 360 .50 \$100,000 \$599.55 0 months int./month monthly pmt (30 x 12) (6 / 12)
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468-2 - Chapter 2 INTEREST RATES Nominal Interest Rates...

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