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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
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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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