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Sarah secured a bank loan of $165,000 for the purchase of a house. The mortgage is...

Sarah secured a bank loan of $165,000 for the purchase of a house. The mortgage is to be amortized through monthly payments for a term of 15 years, with an interest rate of 3%/year compounded monthly on the unpaid balance. She plans to sell her house in 10 years. How much will Sarah still owe on her house at that time? (Round your answer to the nearest cent.)
$

Solutions

Expert Solution

EMI = Loan / PVAF(r%, n)

PVAF = Sum [ PVF(r%, n)]

EMI = Loan / PVAF(r%, n)

= $ 165,000 / PVAF ( 0.25% , 180)

= $ 165,000 / 144.8055

= $ 1139.46

Loan AMortozation:

Month Opening Bal Instalment Int Principal repay Closing Bal
1 $ 1,65,000.00 $ 1,139.46 $ 412.50 $ 726.96 $ 1,64,273.04
2 $ 1,64,273.04 $ 1,139.46 $ 410.68 $ 728.78 $ 1,63,544.26
3 $ 1,63,544.26 $ 1,139.46 $ 408.86 $ 730.60 $ 1,62,813.66
4 $ 1,62,813.66 $ 1,139.46 $ 407.03 $ 732.43 $ 1,62,081.24
5 $ 1,62,081.24 $ 1,139.46 $ 405.20 $ 734.26 $ 1,61,346.98
6 $ 1,61,346.98 $ 1,139.46 $ 403.37 $ 736.09 $ 1,60,610.89
7 $ 1,60,610.89 $ 1,139.46 $ 401.53 $ 737.93 $ 1,59,872.96
8 $ 1,59,872.96 $ 1,139.46 $ 399.68 $ 739.78 $ 1,59,133.18
9 $ 1,59,133.18 $ 1,139.46 $ 397.83 $ 741.63 $ 1,58,391.55
10 $ 1,58,391.55 $ 1,139.46 $ 395.98 $ 743.48 $ 1,57,648.07
11 $ 1,57,648.07 $ 1,139.46 $ 394.12 $ 745.34 $ 1,56,902.73
12 $ 1,56,902.73 $ 1,139.46 $ 392.26 $ 747.20 $ 1,56,155.53
13 $ 1,56,155.53 $ 1,139.46 $ 390.39 $ 749.07 $ 1,55,406.46
14 $ 1,55,406.46 $ 1,139.46 $ 388.52 $ 750.94 $ 1,54,655.52
15 $ 1,54,655.52 $ 1,139.46 $ 386.64 $ 752.82 $ 1,53,902.69
16 $ 1,53,902.69 $ 1,139.46 $ 384.76 $ 754.70 $ 1,53,147.99
17 $ 1,53,147.99 $ 1,139.46 $ 382.87 $ 756.59 $ 1,52,391.40
18 $ 1,52,391.40 $ 1,139.46 $ 380.98 $ 758.48 $ 1,51,632.92
19 $ 1,51,632.92 $ 1,139.46 $ 379.08 $ 760.38 $ 1,50,872.54
20 $ 1,50,872.54 $ 1,139.46 $ 377.18 $ 762.28 $ 1,50,110.26
21 $ 1,50,110.26 $ 1,139.46 $ 375.28 $ 764.18 $ 1,49,346.08
22 $ 1,49,346.08 $ 1,139.46 $ 373.37 $ 766.09 $ 1,48,579.99
23 $ 1,48,579.99 $ 1,139.46 $ 371.45 $ 768.01 $ 1,47,811.98
24 $ 1,47,811.98 $ 1,139.46 $ 369.53 $ 769.93 $ 1,47,042.05
25 $ 1,47,042.05 $ 1,139.46 $ 367.61 $ 771.85 $ 1,46,270.19
26 $ 1,46,270.19 $ 1,139.46 $ 365.68 $ 773.78 $ 1,45,496.41
27 $ 1,45,496.41 $ 1,139.46 $ 363.74 $ 775.72 $ 1,44,720.69
28 $ 1,44,720.69 $ 1,139.46 $ 361.80 $ 777.66 $ 1,43,943.03
29 $ 1,43,943.03 $ 1,139.46 $ 359.86 $ 779.60 $ 1,43,163.43
30 $ 1,43,163.43 $ 1,139.46 $ 357.91 $ 781.55 $ 1,42,381.88
31 $ 1,42,381.88 $ 1,139.46 $ 355.95 $ 783.51 $ 1,41,598.37
32 $ 1,41,598.37 $ 1,139.46 $ 354.00 $ 785.46 $ 1,40,812.91
33 $ 1,40,812.91 $ 1,139.46 $ 352.03 $ 787.43 $ 1,40,025.48
34 $ 1,40,025.48 $ 1,139.46 $ 350.06 $ 789.40 $ 1,39,236.09
35 $ 1,39,236.09 $ 1,139.46 $ 348.09 $ 791.37 $ 1,38,444.72
36 $ 1,38,444.72 $ 1,139.46 $ 346.11 $ 793.35 $ 1,37,651.37
37 $ 1,37,651.37 $ 1,139.46 $ 344.13 $ 795.33 $ 1,36,856.04
38 $ 1,36,856.04 $ 1,139.46 $ 342.14 $ 797.32 $ 1,36,058.72
39 $ 1,36,058.72 $ 1,139.46 $ 340.15 $ 799.31 $ 1,35,259.40
40 $ 1,35,259.40 $ 1,139.46 $ 338.15 $ 801.31 $ 1,34,458.09
41 $ 1,34,458.09 $ 1,139.46 $ 336.15 $ 803.31 $ 1,33,654.78
42 $ 1,33,654.78 $ 1,139.46 $ 334.14 $ 805.32 $ 1,32,849.46
43 $ 1,32,849.46 $ 1,139.46 $ 332.12 $ 807.34 $ 1,32,042.12
44 $ 1,32,042.12 $ 1,139.46 $ 330.11 $ 809.35 $ 1,31,232.77
45 $ 1,31,232.77 $ 1,139.46 $ 328.08 $ 811.38 $ 1,30,421.39
46 $ 1,30,421.39 $ 1,139.46 $ 326.05 $ 813.41 $ 1,29,607.98
47 $ 1,29,607.98 $ 1,139.46 $ 324.02 $ 815.44 $ 1,28,792.54
48 $ 1,28,792.54 $ 1,139.46 $ 321.98 $ 817.48 $ 1,27,975.06
49 $ 1,27,975.06 $ 1,139.46 $ 319.94 $ 819.52 $ 1,27,155.54
50 $ 1,27,155.54 $ 1,139.46 $ 317.89 $ 821.57 $ 1,26,333.97
51 $ 1,26,333.97 $ 1,139.46 $ 315.83 $ 823.62 $ 1,25,510.35
52 $ 1,25,510.35 $ 1,139.46 $ 313.78 $ 825.68 $ 1,24,684.66
53 $ 1,24,684.66 $ 1,139.46 $ 311.71 $ 827.75 $ 1,23,856.91
54 $ 1,23,856.91 $ 1,139.46 $ 309.64 $ 829.82 $ 1,23,027.10
55 $ 1,23,027.10 $ 1,139.46 $ 307.57 $ 831.89 $ 1,22,195.20
56 $ 1,22,195.20 $ 1,139.46 $ 305.49 $ 833.97 $ 1,21,361.23
57 $ 1,21,361.23 $ 1,139.46 $ 303.40 $ 836.06 $ 1,20,525.18
58 $ 1,20,525.18 $ 1,139.46 $ 301.31 $ 838.15 $ 1,19,687.03
59 $ 1,19,687.03 $ 1,139.46 $ 299.22 $ 840.24 $ 1,18,846.79
60 $ 1,18,846.79 $ 1,139.46 $ 297.12 $ 842.34 $ 1,18,004.44
61 $ 1,18,004.44 $ 1,139.46 $ 295.01 $ 844.45 $ 1,17,160.00
62 $ 1,17,160.00 $ 1,139.46 $ 292.90 $ 846.56 $ 1,16,313.44
63 $ 1,16,313.44 $ 1,139.46 $ 290.78 $ 848.68 $ 1,15,464.76
64 $ 1,15,464.76 $ 1,139.46 $ 288.66 $ 850.80 $ 1,14,613.96
65 $ 1,14,613.96 $ 1,139.46 $ 286.53 $ 852.92 $ 1,13,761.04
66 $ 1,13,761.04 $ 1,139.46 $ 284.40 $ 855.06 $ 1,12,905.98
67 $ 1,12,905.98 $ 1,139.46 $ 282.26 $ 857.19 $ 1,12,048.79
68 $ 1,12,048.79 $ 1,139.46 $ 280.12 $ 859.34 $ 1,11,189.45
69 $ 1,11,189.45 $ 1,139.46 $ 277.97 $ 861.49 $ 1,10,327.96
70 $ 1,10,327.96 $ 1,139.46 $ 275.82 $ 863.64 $ 1,09,464.32
71 $ 1,09,464.32 $ 1,139.46 $ 273.66 $ 865.80 $ 1,08,598.52
72 $ 1,08,598.52 $ 1,139.46 $ 271.50 $ 867.96 $ 1,07,730.56
73 $ 1,07,730.56 $ 1,139.46 $ 269.33 $ 870.13 $ 1,06,860.43
74 $ 1,06,860.43 $ 1,139.46 $ 267.15 $ 872.31 $ 1,05,988.12
75 $ 1,05,988.12 $ 1,139.46 $ 264.97 $ 874.49 $ 1,05,113.63
76 $ 1,05,113.63 $ 1,139.46 $ 262.78 $ 876.68 $ 1,04,236.95
77 $ 1,04,236.95 $ 1,139.46 $ 260.59 $ 878.87 $ 1,03,358.09
78 $ 1,03,358.09 $ 1,139.46 $ 258.40 $ 881.06 $ 1,02,477.02
79 $ 1,02,477.02 $ 1,139.46 $ 256.19 $ 883.27 $ 1,01,593.75
80 $ 1,01,593.75 $ 1,139.46 $ 253.98 $ 885.48 $ 1,00,708.28
81 $ 1,00,708.28 $ 1,139.46 $ 251.77 $ 887.69 $    99,820.59
82 $    99,820.59 $ 1,139.46 $ 249.55 $ 889.91 $    98,930.68
83 $    98,930.68 $ 1,139.46 $ 247.33 $ 892.13 $    98,038.55
84 $    98,038.55 $ 1,139.46 $ 245.10 $ 894.36 $    97,144.19
85 $    97,144.19 $ 1,139.46 $ 242.86 $ 896.60 $    96,247.59
86 $    96,247.59 $ 1,139.46 $ 240.62 $ 898.84 $    95,348.75
87 $    95,348.75 $ 1,139.46 $ 238.37 $ 901.09 $    94,447.66
88 $    94,447.66 $ 1,139.46 $ 236.12 $ 903.34 $    93,544.32
89 $    93,544.32 $ 1,139.46 $ 233.86 $ 905.60 $    92,638.72
90 $    92,638.72 $ 1,139.46 $ 231.60 $ 907.86 $    91,730.85
91 $    91,730.85 $ 1,139.46 $ 229.33 $ 910.13 $    90,820.72
92 $    90,820.72 $ 1,139.46 $ 227.05 $ 912.41 $    89,908.31
93 $    89,908.31 $ 1,139.46 $ 224.77 $ 914.69 $    88,993.63
94 $    88,993.63 $ 1,139.46 $ 222.48 $ 916.98 $    88,076.65
95 $    88,076.65 $ 1,139.46 $ 220.19 $ 919.27 $    87,157.38
96 $    87,157.38 $ 1,139.46 $ 217.89 $ 921.57 $    86,235.82
97 $    86,235.82 $ 1,139.46 $ 215.59 $ 923.87 $    85,311.95
98 $    85,311.95 $ 1,139.46 $ 213.28 $ 926.18 $    84,385.77
99 $    84,385.77 $ 1,139.46 $ 210.96 $ 928.50 $    83,457.27
100 $    83,457.27 $ 1,139.46 $ 208.64 $ 930.82 $    82,526.45
101 $    82,526.45 $ 1,139.46 $ 206.32 $ 933.14 $    81,593.31
102 $    81,593.31 $ 1,139.46 $ 203.98 $ 935.48 $    80,657.83
103 $    80,657.83 $ 1,139.46 $ 201.64 $ 937.82 $    79,720.02
104 $    79,720.02 $ 1,139.46 $ 199.30 $ 940.16 $    78,779.86
105 $    78,779.86 $ 1,139.46 $ 196.95 $ 942.51 $    77,837.35
106 $    77,837.35 $ 1,139.46 $ 194.59 $ 944.87 $    76,892.48
107 $    76,892.48 $ 1,139.46 $ 192.23 $ 947.23 $    75,945.25
108 $    75,945.25 $ 1,139.46 $ 189.86 $ 949.60 $    74,995.66
109 $    74,995.66 $ 1,139.46 $ 187.49 $ 951.97 $    74,043.69
110 $    74,043.69 $ 1,139.46 $ 185.11 $ 954.35 $    73,089.34
111 $    73,089.34 $ 1,139.46 $ 182.72 $ 956.74 $    72,132.60
112 $    72,132.60 $ 1,139.46 $ 180.33 $ 959.13 $    71,173.47
113 $    71,173.47 $ 1,139.46 $ 177.93 $ 961.53 $    70,211.95
114 $    70,211.95 $ 1,139.46 $ 175.53 $ 963.93 $    69,248.02
115 $    69,248.02 $ 1,139.46 $ 173.12 $ 966.34 $    68,281.68
116 $    68,281.68 $ 1,139.46 $ 170.70 $ 968.76 $    67,312.92
117 $    67,312.92 $ 1,139.46 $ 168.28 $ 971.18 $    66,341.74
118 $    66,341.74 $ 1,139.46 $ 165.85 $ 973.61 $    65,368.14
119 $    65,368.14 $ 1,139.46 $ 163.42 $ 976.04 $    64,392.10
120 $    64,392.10 $ 1,139.46 $ 160.98 $ 978.48 $    63,413.62
121 $    63,413.62 $ 1,139.46 $ 158.53 $ 980.93 $    62,432.69
122 $    62,432.69 $ 1,139.46 $ 156.08 $ 983.38 $    61,449.32
123 $    61,449.32 $ 1,139.46 $ 153.62 $ 985.84 $    60,463.48
124 $    60,463.48 $ 1,139.46 $ 151.16 $ 988.30 $    59,475.18
125 $    59,475.18 $ 1,139.46 $ 148.69 $ 990.77 $    58,484.41
126 $    58,484.41 $ 1,139.46 $ 146.21 $ 993.25 $    57,491.16
127 $    57,491.16 $ 1,139.46 $ 143.73 $ 995.73 $    56,495.43

Bal after 10 years is $ 63,413.62

jeff jeffy answered 4 months ago
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