1. 1. a) $67,631.83   b) $33,511.96   c) $109,635.81   d) $35,556.87
2. $14,066.19
3. $15,021.08
4. 1. a) $43,307.02   b) $28,620.00   c) $14,687.02
5. $112,179.12
6. 1. a) $26,734.40   b) $11,382.03   c) $49,426.12   d) $27,251.38
7. 1. a) $20,587.31   b) $2,212.69
8. a.      $2,818.12        b.         $481.88
9. $9,443.94 if you assume the first withdrawal occurs 10 years and three (3) months from today or $9,685.94 if you assume that the first withdrawal occurs at the 10-year point.
10. 1. a) $140,461.30   b) $8,357.02   c) $110,460.68
11. 1. a) $1,250.01   b) $43.36   c) $117.93   d) $193.00
12. $962.21
13. $92.02
14. n = 15.58 → 16 quarters n = 41.5 → 42 months[ n = 9.72→ 10 weeks n = 18.51→ 19 semi-annual periods
15. Payments are indefinite because the withdrawals are less than the interest accumulated for the period.
16. 11.2269% compounded monthly
17. 6.8381% compounded monthly
18. 15.2222% compounded monthly = 16.3305% effective
19. $3,816.00 total savings
20. n = 24.84→ 25 quarters or 75 months
21. $38,933.32
22. $51,094.94
23. 123 months at $3,750 and one (1) month at a smaller amount
24. 1. a) $860.03   b) $67,097.29   c) $257,998 with the last payment= $849.03   d) $257.998 − 75,000 = $182,998
25. 19.7469% effective
26. 1. a) $26,078.85 (rounded up)   b) $14,700.73   c) $282,636.43 d):

    Pmt#	Amount	Interest	Principal	Balance
    0				$325,000.00
    1	$26,078.85	$16,250.00	$9,828.85	315,171.15
    2	26,078.85	15,758.56	10,320.29	304,850.85
    3	26,078.85	15,242.54	10,836.31	294,014.55
    4	26,078.85	14,700.73	11,378.12	282,636.43

27. 1. a) 82 full payments and one (1) smaller payment   b) $2,266.47   c) $1,058.99   d) 44.4%   e) $79,066.47
28. 1. a) PV of monthly payments= $1,007,279.88 which is more than the $1 million cash payment. Choose the payments.   b) PV of monthly payments= $991,342.82 which is less than the $1 million cash payment. Choose the $1 million cash payment.
29. PV =  $18,794.90;  FV = $46,021.60
30. PV =  $52,476.38;  FV = $182,913.49
31. 1. a) $8,477.78   b) $10,800.00   c) $2,322.22
32. $47,360.41
33. 1. a) $2,100.12   b) $10,800.00   c) $2,322.22
34. 1. a) 11.9930%   b) compounded monthly = 12.6747% effective
35. 16.1008% compounded quarterly
36. $617.43
37. n = 185.9986 → 186 monthly payments (15 years and 6 months)
38. $7,477.38, assuming that the first payment occurs at year two
39. $5,673.21, assuming that the first payment occurs at 12 months
40. $795.49 with first payment at year eight
41. $29,439.84, assuming that there are eight years of payments (for example, n = 32)
42. $235,294.12
43. $545,454.55
44. 1. a) $217.86   b) $221.35
45. $557.06
46. 1. a) $6,264.61   b) $7,200.00   c) $935.39
47. $173,428.57
48. 1. a) $26,370.83   b) $10,370.83
49. 1. a) $676.16 (rounded up)   b) $46,036.44   c) $162,261.81 with the last payment= $659.57   d) $162,261.81 − $48,600 = $113,661.81
50. $50,447.62
51. 1. a) $608.72 (rounded up)   b) $61,465.87   c) $182,606.20   d) $107,606.20
52. $112,175.55
53. $5.5 years, $8,450 interest earned
54. 1. a) 5 years   b) $2,761.02
55. 11 years
56. 1. a) 40 years and $192,040 of interest   b) b. You never will, since the payment only covers the interest.
57. $27,402.55
58. $1,766.18
59. $66,820.18
60. $152,996.91
61. $48,752.43
62. 1. a) $4,143.48   b) $1,206.71−$1,000 = $206.71 per month
63. 1. a) $1,692.10   b) $1,692.10 ×120 − $200 × 240 = $155,052
64. 1. a) $66/month   b) $2,250 × 180− $66 ×540 = $369,360
65. 1. a) $695.09   b) $50,000 − $695.09 × 60 = $8,294.60
66. 1. a) $48,559.18   b) $2,500 × 60 − $48,559.18 = $101,440.82
67. 1. a) $25,000   b) $27,000
68. 1. a) $50,583.41   b) $918.93 per month
69. $720.87
70. $1,000
71. $1,000,000
72. $25,000
73. 1. a) $50.00/share   b) a loss of $18.75/share
74. 1. a) $6,500   b) Gain of $1,500.
75. 1. a) The PV of the $7,000 perpetual payment is $1,400,000, so $1,500,000 today is better   b) $7,500 per month forever
76. $496.74 per month
77. 1. a) i.    $706.23/month     ii. $688.03/month   b) $873.60
78. $150,000 less
79. 1. a) $6,600   b) $3,400 gain
80. 1. a) i.  1% per month    ii.  0.975879417% per month   b) $2,000 for the 1st month 1% per month and only $1951.76 using 0.975879417% per month.

81. Period	Payment PMT	Interest INT	Principal Paid-PRN	Balance Owing-BAL
    0				$1,200.00
    1	$350	$12.00	$338.00	862.00
    2	350	8.62	341.38	520.62
    3	350	5.21	344.79	175.83
    4	175.83 + 1.76 = $177.59	1.76	175.83	0
    TOTAL		$27.59	$1,200.00

    Final payment is $350−$172.42 = $177.58 using the calculator (slight difference due to rounding).

82. 1. a) 1240.74 → $1241.00/month   b) n = 239.8969885   c) 1st month: $332.35 principal, $908.65 interest 60th month: $459.53 principal, $781.47 interest   d) Principal paid off= $4,111.26: Interest is $10,780.74   e) e. $8,502.60/ $165,000 = 5.153%   f) Principal paid off= $23,554.39: Interest is $50,905.61   g) Principal paid off= $5,351.30: Interest is $9,540.70   h) Would need $141,445.61 to pay it all off   i) $1,113.48
83. 1. a) $196,200 rounded   b) $1,341.82 → $1,342/month   c) $62,591.48   d) $177,071.48   e) $1,154.254 – $1,155/month   f) $813.47
84. 1. a) 137,283.97…, $137,300 (rounded)    b) $895.95 …, $896/month   c) $26,478.31   d) $5,777.69/$123,000 = 4.697%   e) $8,683.64   f) 939.527 …, $940/month; The balance outstanding is $107,222.31   g) $545.58
85. 1. a) $1,920.00 per month   b) 447.8742287/26 = 17.2259 years, so save 25 years – 17.23 years = 7.77 years The interest savings is: $1,920 × 300- $960 × 447.8742287 = $146,041
86. 1. a) $3,000 (n = 299.8201542)   b) $2,430.53   c) $29,143.82   d) $77,273.24  ($452,806.23 −$375,532.99)   e) $2,982   f) $2,737.26
87. $519,290.79,  $519,300
88.  a) $3,205 (n = 299.8729184)   b) 6.056% ($31,492.35/$520,000)   c) $26,748.44   d) $14,419.50   e) $3,410   f) $3,297.03
89. $76,785.12 ($421,860.24- $345,075.12)
90. 1. a) $550   b) $5875
91. 13.58942%
92. $36,994.34
93. 30 months
94. $5,100
95. 1. a.) $21,000   b.) $2,801.84
96. 1. a.) $3,780   b.) $1,756
97. j₂ = 9.38064%
98. $181,818.18
99. $225,394.44
100. $24,271.84
101. $26.75/share
102. 1. a.) $1,177.37   b.) $428,073.40
103. a) $271.00/month  b) $ 139,186.53
104. $238,086.11
105. 150 months or 12.5 years
106. $500/month
107. $177,755.87
108. $30,723.99
109. $136,300.67
110. $44,449.82
111. $19,855.69
112. $352.39/month
113. $188,830.07
114. Month-end: $302,244.75   Year-end: $290,846.96   $11,397.79 more
115. $223,904.53

 

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