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SOLUTIONS CHAPTER 9

# SOLUTIONS CHAPTER 9 - CHAPTER 9 TIME VALUE OF MONEY 9.1 To...

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CHAPTER 9 TIME VALUE OF MONEY 9.1 To find the future value of a current present value, use FV n = PV x FVIF n,i . BY TABLE (a) FV 10 = \$2,000 x FVIF 10,8% = \$2,000 x 2.159 = \$4,318 (b) FV 40 = \$2,000 x FVIF 40,2% = \$2,000 x 2.208 = \$4,416 (c) FV 40 = \$2,000 x FVIF 40,3% = \$2,000 x 3.262 = \$6,524 BY FINANCIAL CALCULATOR (a) \$4317.85 (b) \$4416.07 (c) \$6524.07 (d) \$6638.92 (e) \$6640.00 9-2 To find the future value of an annuity, use FVA = CF x FVAIF n,i . (a) FVA = \$3,000 x FVAIF 10,8% = \$3,000 x 14.487 = \$43,461 (b) FVA = \$1,500 x FVAIF 20,4% = \$1,500 x 29.778 = \$44,667 (c) FVA = \$ 100 x FVAIF 120,.667% = \$ 18294.60 (by financial calculator) 9-3 To find the present value of a future value, use PV = FV x PVIF n,i . (a) PV = \$1,000 x PVIF 10,6% = \$1,000 x 0.558 = \$ 558 (b) PV = \$2,000 x PVIF 10,3% = \$2,000 x 0.744 = \$1,488 (c) \$1215.58 (by financial calculator) 9-4 To find the present value of an annuity, use PVA = CF x PVAIF n,i . (a) PVA = \$2,000 x PVAIF 10,8% = \$2,000 x 6.71 = \$13,420 and by financial calculator, \$13420.16 (b) PVA = \$2,000 x PVAIF 20,5% = \$2,000 x 12.462 = \$24,924 and by financial calculator, \$24924.42 (c) PVA = \$3,000 x PVAIF 48,1% or by financial calculator, \$113921.88. 9.5 ANNUAL COMPOUNDING

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To solve this problem, use either FV n = PV x FVIF n,i or PV = FV n x PVIF n,i . \$3 = \$1 x FVIF n,6% ; FVIF n,6% = 3; Table A shows that to triple \$1 at 6 percent, it takes slightly less than 19 years. \$1 = \$3 x PVIF n,6% ; PVIF n,6% = 0.333; Table C shows that to triple \$1 at 6 percent, it takes slightly less than 19 years. Or by financial calculator, 18.85 years COMPOUNDING (by financial calculator) Semiannual 18.58 years Quarterly 18.44 years Monthly 18.36 years Daily 18.31 years 9-6 To solve this problem, use CF = PVA ÷ PVAIF n,i . CF = \$20,000 ÷ PVAIF 20,2% = \$20,000 ÷ 16.351 = \$1,223 Or by financial calculator, \$1223.13 . 9-7 To determine the interest rate of the note, use PVAIF n,i = PVA / CF. PVAIF 4,i = \$10,161 ÷ \$3,000 = 3.387; Table D shows that the interest rate of the note is 7 percent. Or, by financial calculator, 7.0028%. 9-8 PVIF n,1% = \$15,000 ÷ \$383 = 39.164; Table D shows that it will take 50 months to pay the balance and the interest. Or by financial calculator: 49.95 Months 9-9 Bond Value = CF x PVAIF n,i + FV n x PVIF n,i = \$60 x PVAIF 40,5% + \$1,000 x PVIF 40,5% = \$60 x 17.159 + \$1,000 x 0.142 = \$1,171.54 Or, by financial calculator, \$1171.59. 9-10 PV = \$200 x 0.909 + \$300 x 0.826 + \$400 x 0.751 = \$730 9-11 PVA = \$20,000 x PVAIF 10,10% x PVIF 15,10% = \$20,000 x 6.145 x 0.239 = \$29,373 Or by financial calculator: \$29,419.21
9-12 PVA = \$10,000 x PVAIF 9,10% = \$10,000 x 5.759 = \$57,590 Or by financial calculator: \$57,590.24 9-13 a) \$1,330.61 per month b) Month Balance Principal Interest 1 \$199839.06 \$163.94 \$1166.67 2 \$199671.17 \$164.89 \$1165.70 3 \$199505.31 \$165.86 \$1164.75 c) Principal = \$73524.67; Interest = \$220539.03 d) \$467.05 = new payment of \$1797.66 less old payment of \$1330.61 Savings: 30 year loan cost (\$1330.61 x 360) or \$479019.60 15 year loan cost (\$1797.66 x 180) or \$323578.80 DIFFERENCE \$155440.80 9-14 PVA = \$100,000 x (1 + PVAIF 9,12% ) = \$100,000 x (1 + 5.328) = \$632,800 Or solving for the annuity due by financial calculator: \$632824.98 Dan should take the \$700,000 because it is greater than the present value of the \$100,000 annuity (\$632,824.98). 9-15 You have to solve this problem in two steps. First, you must determine how much you need to have at age 65 to provide a 20-year monthly payment of \$3,000, given the 10 percent rate of return.

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