Chapter 4 Review Question Solutions

  1. Time Interest Balances:
    0m $8,000.00
    3m $200.00 $8,200.00
    6m $205.00 $8,405.00
    9m $210.13 $8,615.13
    12m $215.37 $8,830.50
  2. Time Interest Balances:
    0m $12,000.00
    lm $150.00 $12,150.00
    2m $151.88 $12,301.88
    3m $153.77 $12,455.65
    4m $155.70 $12,611.35
    5m $157.64 $12,768.99
  3. Nominal Rate Frequency Nominal Rate, jm Periodic rate, i
    8% semi-annually j2 = 0.08 i =0.04
    15% monthly j12 = 0.15 i = 0.0125
    10% quarterly j4 = 0.10 i= 0.025
    9% annually j1 = 0.09 i= 0.09
    10.4% weekly j52 = 0.104 i= 0.002
  4. Nominal Rate Compounding Frequency Nominal Rate, jm Periodic Rate, i
    7% annually jl = 7% i= 0.07
    9% quarterly j4 = 9% i = 0.0225
    6% monthly j12 = 6% i = 0.005
    12% quarterly j4 = 12% i = 0.03
    24% monthly j12 = 24% i = 0.02
    17% semi-annually j2 = 17% i = 0.085
  5. PV Interest Rate Length i n FV
    $11,500 9% quarterly 2 years 0.0225 8 $13,740.56
    $7,400 6% annually 4 years 0.06 4 $9,342.33
    $14,000 8.6% monthly 8 months 0.007166 8 $14,823.09
  6.             Year Interest Balances
    0 $1,000.00
    1 $85.00 $1,085.00
    2 $92.23 $1,177.23
    3 $100.06 $1,277.29
  7. $31,459.10
  8. a.            Year Balance
    0 $1,000.00
    1 $1,250.00
    2 $1,562.50
    3 $1,953.13
    4 $2,441.41
    5 $3,051.76
    6 $3,814.70
    7 $4,768.38
    b.        Year Balance
    0 $1,000.00
    1 $1,250.00
    2 $1,500.00
    3 $1,750.00
    4 $2,000.00
    5 $2,250.00
    6 $2,500.00
    7 $2,750.00
  9. PV Interest Rate Length n FV
    $11,500 6.5% compounded semi-annually 2 years 8 $11,364.76
    $7,400 16% compounded monthly 3.5 years 4 $25,000.00
    $14,000 I0% compounded quarterly 1 year 8 $30,000.00
    1. (a)$38,980.40 (b) $39,959.34
    2. $40,963.72
  11. $5,591.10
  12. Year Balance
    1 $81,000.00
    2 $54,910.00
    3 $60,950.10

    b. $100,000 (1.11)3 = $30,000 (1.11)2 + $35,000 (1.11) + x x  = $60,950.10

  13. a. $37,684.65     b. $38,876.54
    1. (a) $23,685.88 (b) FV = $ 23,685(1.07)1.5 =$ 20,000(1.07)4 =$ 26,215.92
    1. (a) 8% compounded quarterly (b)8.08% compounded semi-annually
  16. 16% compounded quarterly = 15.7913% compounded monthly
  17. Effective Rate, j1 j2 j4 j12
    17.227080% 16.214281% 16.542910% 16%
    12.550881% 12.180000% 12% 11.881961%
    9.202500% 9% 8.900966% 8.835748%
    1. (a) $5,076.94 (b) $5,076.94 (c) $5,076.94 (d) $5,076.94 (using a fractional period )
  19. $4,416.96
  20. $6,400.42
  21. $2,868.47
  22. $11,506.98
  23. $590,856.82
    1.  (a) $126,934.31 (b) 8.82331% (c)  37.65 years
  25. j4 = 21.44411%
    1.  (a) j12 = 10.17956% (b)  j4  = 10.26616% (c)  j2 = 10.39790% (d)  j1 = 10.66819%
  27. 5.5 years
  28. 5.0 years
  29. 7.0000%
  30. 1.5 years
  31. $7,457.11 (the interest earned is $2,457.11)
  32. $10,000 (the interest paid is $15,292.49)
  33. In today’s dollars, the 2nd option is worth $17,708.60  which is less than $18,000 so the second option is cheaper
  34. $6,441.19
  35. $3,284.78
  36. $21,051.50
  37. $10,757.36
    1. (a) Payment= $1,396.46 (b) the interest paid is $1,189.38
  39.    First payment: $8,083.05; second payment $11,083.05
  40. a. $359,500   b.      $46,000
  41. j1 = 20.2705% (effective means compounded annually)
  42. Canada: j1= 8.57640%; US: j1 = 8.62314%, Canadian bank is the better deal
  43. j1 = 15.86504%
  44. j2 = 8.08%
  45. j4 = 8.05345%
  46. j1 = 8.29995%
  47. j1 = 4.062377967%,  not 4.07%
  48. j12 = 9.79782%
  49. 21.550625%
    1. (a) CSB: $5,970.10   GIC: $6,039.45 (b) CSB: j1= 6.08904%;    GIC: j1 = 6.49825%
    1.  (a) $8,134.05 (b) $2,134.05 (c) j2 = 5.14246% (d) j1 = 10.40895137%
  52. j4 = 7.58458%
  53. j12 = 10.49364%
  54. 8.08142% compounded annually

 

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