A the amount of the annuity in dollars r annual

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A = the amount of the annuity (in dollars). r = annual interest rate ÷ number of times interest paid per year n = number of times interest paid per year times number of years 18/10/17 Fixed Income Securities 37 ( ) 1 1 Ρ Τ + = ΢ Υ Σ Φ n n r P A r
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Reviewing Time Value Example of Future Value of an Ordinary Annuity Using Annual Interest: If A = $2,000,000, r = 0.08, and n = 15, then P n = ? P n = $2,000,000 [27.152125] = $54,304,250 18/10/17 Fixed Income Securities 38 ( ) 1 1 Ρ Τ + = ΢ Υ Σ Φ n n r P A r ( ) 15 1 0.08 1 $2,000,000 0.08 Ρ Τ + = ΢ Υ Σ Φ n P
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Reviewing Time Value Future Value of an Ordinary Annuity Using Semiannual Interest : If A = $2,000,000/2 = $1,000,000, r = 0.08/2 = 0.04 and n = 15(2) = 30, then P n = ? P n = $1,000,000 [56.085] = $56,085,000 18/10/17 Fixed Income Securities 39 ( ) 1 1 Ρ Τ + = ΢ Υ Σ Φ n n r P A r ( ) 30 1 0.04 1 $1,000,000 0.04 Ρ Τ + = ΢ Υ Σ Φ n P
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Reviewing Time Value The Present Value is the future value process in reverse. o A = the amount of the annuity (in dollars) o r = annual interest rate ÷ number of times interest paid per year o n = number of times interest paid per year times number of years o For a given future value at a specified time in the future, the higher the interest rate (or discount rate), the lower the present value. o For a given interest rate, the further into the future that the future value will be received, then the lower its present value. 18/10/17 Fixed Income Securities 40 ( ) 1 1/ 1 Ρ Τ + = ΢ Υ Σ Φ n r PV A r ( ) Υ Φ Τ ΢ Σ Ρ + = n n r P PV 1 1 or in case of annuity
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Reviewing Time Value Present Value of an Ordinary Annuity (PV) using Annual Interest: If A = $100, r = 0.09, and n = 8, then PV = ? PV = $100 [5.534811] = $553.48 18/10/17 Fixed Income Securities 41 ( ) 1 1/ 1 Ρ Τ + = ΢ Υ Σ Φ n r PV A r ( ) 8 1 1/ 1 0.09 $100 0.09 Ρ Τ + = ΢ Υ Σ Φ PV
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