53 Present Values 515 Semiannual and Other Compounding Perio

5-3: Present Values 5-15: Semiannual and Other Compounding Periods Present value for vaious discounting periods Find the present value of $500 due in the future under each of these conditions: a. 14% nominal rate, semiannual compounding, discounted back 8 years. Round your answer to the nearest cent. b.14% nominal rate, quarterly compounding, discounted back 8 years. Round your answer to the nearest cent. c. 14% nominal rate, monthly compounding, discounted back 1 year. Round your answer to the nearest cent.

Solution

a. Present Value $ 169.37 Working: Present Value = Future Value x Present Value of 1 = $        500 x 0.338735 = $ 169.37 Present Value of 1 = (1+i)^-n Where, = (1+0.07)^-16 i 14%/2 = 7% = 0.338735 n 8*2 = 16 b. Present Value $ 166.29 Working: Present Value = Future Value x Present Value of 1 = $        500 x 0.33259 = $ 166.29 Present Value of 1 = (1+i)^-n Where, = (1+0.035)^-32 i 14%/4 = 3.5% = 0.33259 n 8*4 = 32 c. Present Value $ 435.01 Working: Present Value = Future Value x Present Value of 1 = $        500 x 0.870029 = $ 435.01 Present Value of 1 = (1+i)^-n Where, = (1+0.01167)^-12 i 14%/12 = 1.167% = 0.870029 n 1*12 = 12