In: Finance
Problem 4-29
Loan Amortization
Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $40,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10%, but it calls for payments every 6 months, beginning on June 30, and is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year?
$
Total amount of interest paid during first year=665.04
Payment | Loan beginning balance | Payment | Interest payment | Principal payment | Loan ending balance |
1 | 40000 | $528.60 | $333.33 | $195.27 | $39,804.73 |
2 | $39,804.73 | $528.60 | $331.71 | $196.90 | $39,607.83 |
3 | $39,607.83 | $528.60 | $330.07 | $198.54 | $39,409.30 |
4 | $39,409.30 | $528.60 | $328.41 | $200.19 | $39,209.10 |
5 | $39,209.10 | $528.60 | $326.74 | $201.86 | $39,007.24 |
6 | $39,007.24 | $528.60 | $325.06 | $203.54 | $38,803.70 |
7 | $38,803.70 | $528.60 | $323.36 | $205.24 | $38,598.46 |
8 | $38,598.46 | $528.60 | $321.65 | $206.95 | $38,391.51 |
9 | $38,391.51 | $528.60 | $319.93 | $208.67 | $38,182.84 |
10 | $38,182.84 | $528.60 | $318.19 | $210.41 | $37,972.43 |
11 | $37,972.43 | $528.60 | $316.44 | $212.17 | $37,760.26 |
12 | $37,760.26 | $528.60 | $314.67 | $213.93 | $37,546.33 |
13 | $37,546.33 | $528.60 | $312.89 | $215.72 | $37,330.61 |
14 | $37,330.61 | $528.60 | $311.09 | $217.51 | $37,113.09 |
15 | $37,113.09 | $528.60 | $309.28 | $219.33 | $36,893.77 |
16 | $36,893.77 | $528.60 | $307.45 | $221.15 | $36,672.61 |
17 | $36,672.61 | $528.60 | $305.61 | $223.00 | $36,449.62 |
18 | $36,449.62 | $528.60 | $303.75 | $224.86 | $36,224.76 |
19 | $36,224.76 | $528.60 | $301.87 | $226.73 | $35,998.03 |
20 | $35,998.03 | $528.60 | $299.98 | $228.62 | $35,769.41 |
21 | $35,769.41 | $528.60 | $298.08 | $230.52 | $35,538.89 |
22 | $35,538.89 | $528.60 | $296.16 | $232.45 | $35,306.44 |
23 | $35,306.44 | $528.60 | $294.22 | $234.38 | $35,072.06 |
24 | $35,072.06 | $528.60 | $292.27 | $236.34 | $34,835.72 |
25 | $34,835.72 | $528.60 | $290.30 | $238.31 | $34,597.42 |
26 | $34,597.42 | $528.60 | $288.31 | $240.29 | $34,357.12 |
27 | $34,357.12 | $528.60 | $286.31 | $242.29 | $34,114.83 |
28 | $34,114.83 | $528.60 | $284.29 | $244.31 | $33,870.52 |
29 | $33,870.52 | $528.60 | $282.25 | $246.35 | $33,624.17 |
30 | $33,624.17 | $528.60 | $280.20 | $248.40 | $33,375.77 |
31 | $33,375.77 | $528.60 | $278.13 | $250.47 | $33,125.30 |
32 | $33,125.30 | $528.60 | $276.04 | $252.56 | $32,872.74 |
33 | $32,872.74 | $528.60 | $273.94 | $254.66 | $32,618.07 |
34 | $32,618.07 | $528.60 | $271.82 | $256.79 | $32,361.29 |
35 | $32,361.29 | $528.60 | $269.68 | $258.93 | $32,102.36 |
36 | $32,102.36 | $528.60 | $267.52 | $261.08 | $31,841.28 |
37 | $31,841.28 | $528.60 | $265.34 | $263.26 | $31,578.02 |
38 | $31,578.02 | $528.60 | $263.15 | $265.45 | $31,312.57 |
39 | $31,312.57 | $528.60 | $260.94 | $267.66 | $31,044.90 |
40 | $31,044.90 | $528.60 | $258.71 | $269.90 | $30,775.01 |
41 | $30,775.01 | $528.60 | $256.46 | $272.14 | $30,502.86 |
42 | $30,502.86 | $528.60 | $254.19 | $274.41 | $30,228.45 |
43 | $30,228.45 | $528.60 | $251.90 | $276.70 | $29,951.75 |
44 | $29,951.75 | $528.60 | $249.60 | $279.01 | $29,672.75 |
45 | $29,672.75 | $528.60 | $247.27 | $281.33 | $29,391.42 |
46 | $29,391.42 | $528.60 | $244.93 | $283.67 | $29,107.74 |
47 | $29,107.74 | $528.60 | $242.56 | $286.04 | $28,821.70 |
48 | $28,821.70 | $528.60 | $240.18 | $288.42 | $28,533.28 |
49 | $28,533.28 | $528.60 | $237.78 | $290.83 | $28,242.46 |
50 | $28,242.46 | $528.60 | $235.35 | $293.25 | $27,949.21 |
51 | $27,949.21 | $528.60 | $232.91 | $295.69 | $27,653.51 |
52 | $27,653.51 | $528.60 | $230.45 | $298.16 | $27,355.36 |
53 | $27,355.36 | $528.60 | $227.96 | $300.64 | $27,054.72 |
54 | $27,054.72 | $528.60 | $225.46 | $303.15 | $26,751.57 |
55 | $26,751.57 | $528.60 | $222.93 | $305.67 | $26,445.90 |
56 | $26,445.90 | $528.60 | $220.38 | $308.22 | $26,137.67 |
57 | $26,137.67 | $528.60 | $217.81 | $310.79 | $25,826.89 |
58 | $25,826.89 | $528.60 | $215.22 | $313.38 | $25,513.51 |
59 | $25,513.51 | $528.60 | $212.61 | $315.99 | $25,197.52 |
60 | $25,197.52 | $528.60 | $209.98 | $318.62 | $24,878.89 |
61 | $24,878.89 | $528.60 | $207.32 | $321.28 | $24,557.61 |
62 | $24,557.61 | $528.60 | $204.65 | $323.96 | $24,233.66 |
63 | $24,233.66 | $528.60 | $201.95 | $326.66 | $23,907.00 |
64 | $23,907.00 | $528.60 | $199.23 | $329.38 | $23,577.62 |
65 | $23,577.62 | $528.60 | $196.48 | $332.12 | $23,245.50 |
66 | $23,245.50 | $528.60 | $193.71 | $334.89 | $22,910.61 |
67 | $22,910.61 | $528.60 | $190.92 | $337.68 | $22,572.93 |
68 | $22,572.93 | $528.60 | $188.11 | $340.50 | $22,232.43 |
69 | $22,232.43 | $528.60 | $185.27 | $343.33 | $21,889.10 |
70 | $21,889.10 | $528.60 | $182.41 | $346.19 | $21,542.91 |
71 | $21,542.91 | $528.60 | $179.52 | $349.08 | $21,193.83 |
72 | $21,193.83 | $528.60 | $176.62 | $351.99 | $20,841.84 |
73 | $20,841.84 | $528.60 | $173.68 | $354.92 | $20,486.92 |
74 | $20,486.92 | $528.60 | $170.72 | $357.88 | $20,129.04 |
75 | $20,129.04 | $528.60 | $167.74 | $360.86 | $19,768.18 |
76 | $19,768.18 | $528.60 | $164.73 | $363.87 | $19,404.31 |
77 | $19,404.31 | $528.60 | $161.70 | $366.90 | $19,037.41 |
78 | $19,037.41 | $528.60 | $158.65 | $369.96 | $18,667.45 |
79 | $18,667.45 | $528.60 | $155.56 | $373.04 | $18,294.41 |
80 | $18,294.41 | $528.60 | $152.45 | $376.15 | $17,918.26 |
81 | $17,918.26 | $528.60 | $149.32 | $379.28 | $17,538.98 |
82 | $17,538.98 | $528.60 | $146.16 | $382.44 | $17,156.54 |
83 | $17,156.54 | $528.60 | $142.97 | $385.63 | $16,770.90 |
84 | $16,770.90 | $528.60 | $139.76 | $388.85 | $16,382.06 |
85 | $16,382.06 | $528.60 | $136.52 | $392.09 | $15,989.97 |
86 | $15,989.97 | $528.60 | $133.25 | $395.35 | $15,594.62 |
87 | $15,594.62 | $528.60 | $129.96 | $398.65 | $15,195.97 |
88 | $15,195.97 | $528.60 | $126.63 | $401.97 | $14,794.00 |
89 | $14,794.00 | $528.60 | $123.28 | $405.32 | $14,388.68 |
90 | $14,388.68 | $528.60 | $119.91 | $408.70 | $13,979.99 |
91 | $13,979.99 | $528.60 | $116.50 | $412.10 | $13,567.88 |
92 | $13,567.88 | $528.60 | $113.07 | $415.54 | $13,152.34 |
93 | $13,152.34 | $528.60 | $109.60 | $419.00 | $12,733.34 |
94 | $12,733.34 | $528.60 | $106.11 | $422.49 | $12,310.85 |
95 | $12,310.85 | $528.60 | $102.59 | $426.01 | $11,884.84 |
96 | $11,884.84 | $528.60 | $99.04 | $429.56 | $11,455.28 |
97 | $11,455.28 | $528.60 | $95.46 | $433.14 | $11,022.14 |
98 | $11,022.14 | $528.60 | $91.85 | $436.75 | $10,585.38 |
99 | $10,585.38 | $528.60 | $88.21 | $440.39 | $10,144.99 |
100 | $10,144.99 | $528.60 | $84.54 | $444.06 | $9,700.93 |
101 | $9,700.93 | $528.60 | $80.84 | $447.76 | $9,253.17 |
102 | $9,253.17 | $528.60 | $77.11 | $451.49 | $8,801.68 |
103 | $8,801.68 | $528.60 | $73.35 | $455.26 | $8,346.42 |
104 | $8,346.42 | $528.60 | $69.55 | $459.05 | $7,887.37 |
105 | $7,887.37 | $528.60 | $65.73 | $462.87 | $7,424.50 |
106 | $7,424.50 | $528.60 | $61.87 | $466.73 | $6,957.76 |
107 | $6,957.76 | $528.60 | $57.98 | $470.62 | $6,487.14 |
108 | $6,487.14 | $528.60 | $54.06 | $474.54 | $6,012.60 |
109 | $6,012.60 | $528.60 | $50.10 | $478.50 | $5,534.10 |
110 | $5,534.10 | $528.60 | $46.12 | $482.49 | $5,051.62 |
111 | $5,051.62 | $528.60 | $42.10 | $486.51 | $4,565.11 |
112 | $4,565.11 | $528.60 | $38.04 | $490.56 | $4,074.55 |
113 | $4,074.55 | $528.60 | $33.95 | $494.65 | $3,579.90 |
114 | $3,579.90 | $528.60 | $29.83 | $498.77 | $3,081.13 |
115 | $3,081.13 | $528.60 | $25.68 | $502.93 | $2,578.20 |
116 | $2,578.20 | $528.60 | $21.49 | $507.12 | $2,071.09 |
117 | $2,071.09 | $528.60 | $17.26 | $511.34 | $1,559.74 |
118 | $1,559.74 | $528.60 | $13.00 | $515.61 | $1,044.14 |
119 | $1,044.14 | $528.60 | $8.70 | $519.90 | $524.23 |
120 | $524.23 | $528.60 | $4.37 | $524.23 | $0.00 |