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Unformatted text preview: Chapter 4: More Interest Formulas 41 (a) R = $100(F/A, 10%, 4) = $100(4.641) = $464.10 (b) S = 50 ( P/G , 10%, 4) = 50 (4.378) = 218.90 (c) T = 30 ( A/G , 10%, 5) = 30 (1.810) = 54.30 0 1 2 3 4 100 100 100 100 R $10 $15 S T T T T T 30 60 120 0 1 2 3 4 $50 90 42 (a) B = $100 ( P/F , 10%, 1) + $100 ( P/F , 10%, 3) + $100 ( P/F , 10%, 5) = $100 (0.9091 + 0.7513 + 0.6209) = $228.13 (b) $634 = $200 ( P/A , i%, 4) ( P/A , i %, 4) = $634/$200 = 3.17 From compound interest tables, i = 10%. (c) V = $10 ( F/A , 10%, 5)  $10 = $10 (6.105)  $10 = $51.05 $0 $100 $100 B $63 $200 $200 $200 i = ? $10 $10 $10 $10 V (d) $500 = x ( P/A , 10%, 4) + x ( P/G , 10%, 4) $500 = x (3.170 + 4.378) x = $500/7.548 = $66.24 43 (a) C = $25 ( P/G , 10%, 4) = $25 (4.378) = $109.45 (b) $500 = $140 ( P/A , i%, 6) ( P/A , i %, 6) = $500/$140 = 3.571 Performing linear interpolation: $50 $25 $50 $75 2x $50 x 3x 4x $50 A = $140 i = ? ( P/A , i %, 6) i 3.784 15% 3.498 18% i = 15% + (18%  15%) ((3.487 3.571)/(3.784 3.498) = 17.24% (c) F = $25 ( P/G , 10%, 5) ( F/P , 10%, 5) = $25 (6.862) (1.611) = $276.37 (d) A = $40 ( P/G , 10%, 4) ( F/P , 10%, 1) ( A/P , 10%, 4) = $40 (4.378) (1.10) (0.3155) = $60.78 44 (a) $50 $75 W $10 $50 $75 P $10 F P $0 $40 $80 $12 A A A A W = $25 ( P/A , 10%, 4) + $25 ( P/G , 10%, 4) = $25 (3.170 + 4.378) = $188.70 (b) x = $100 ( P/G , 10%, 4) ( P/F , 10%, 1) = $100 (4.378) (0.9091) = $398.00 (c) Y = $300 ( P/A , 10%, 3)  $100 ( P/G , 10%, 3) = $300 (2.487 2.329) = $513.20 (d) Z = $100 ( P/A , 10%, 3)  $50 ( P/F , 10%, 2) = $100 (2.487)  $50 (0.8264) = $207.38 $0 $0 $10 $15 x Y $30 $20 $10 Z $10 $10 $50 45 P = $100 + $150 ( P/A , 10%, 3) + $50 ( P/G , 10%, 3) = $100 + $150 (2.487) + $50 (2.329) = $589.50 46 x = $300 ( P/A , 10%, 5) + $100 ( P/G , 10%, 3) + $100 ( P/F , 10%, 4) = $300 (3.791) + $100 (2.329) + $100 (0.6830) = $1,438.50 47 P = $10 (P/G, 15%, 5) + $40 (P/A, 15%, 4)(P/F, 15%, 1) = $10 (5.775) + $40 (2.855) (0.8696) = $157.06 P $10 $15 $20 $25 x $30 $40 $50 $40 $30 P $0 $50 $60 $80 48 Receipts (upward) at time O : PW = B + $800 (P/A, 12%, 3) = B + $1,921.6 Expenditures (downward) at time O : PW= B (P/A, 12%, 2) + 1.5B (P/F, 12%, 3) = 2.757B Equating: B + $1,921.6 = 2.757B B = $1,921.6/2.757 = $1,093.70 49 F = A (F/A, 10%, n) $35.95 = 1 (F/A, 10%, n) (F/A, 10%, n) = 35.95 From the 10% interest table, n = 16. 410 P = A (P/A, 3.5%, n) $1,000 = $50 (P/A, 3.5%, n) (P/A, 3.5%, n) = 20 From the 3.5% interest table, n = 35. O $800 $800 B B B 1.5B 411 F = $100 (F/A, 10%, 3) = $100 (3.310)= $331 P = $331 (F/P, 10%, 2) = $331 (1.210)= $400.51 J = $400.51 (A/P, 10%, 3) = $400.51 (0.4021) = $161.05 Alternate Solution: One may observe that J is equivalent to the future worth of $100 after five interest periods, or: J = $100 (F/P, 10%, 5) = $100 (1.611)= $161.10 412 P = $100 (P/G, 10%, 4) = $100 (4.378)= $437.80 P = $437.80 (F/P, 10%, 5) = $437.80 (1.611) = $705.30 C = $705.30 (A/P, 10%, 3) = $705.30 (0.4021) = $283.60 $100 $100 $100 F P J J P $10 $20 $30 P C C C 413...
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 Spring '10
 Freeman

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