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See attached.
Loan Project: Buying a House
For this assignment, you will analyze a home mortgage loan.
Task 1: Find a description, asking price, and real estate taxes of a house for sale, and decide on a
purchase price you would be willing to pay (assuming you have the means). Find a current market
interest rate for a 30-year fixed-rate mortgage having a down payment of 20 percent of the purchase
price. [By the end of Week 2, January 27, post your work on Task 1 as a main topic in the Loan
Project conference.]
Task 2: Compute the down payment, amount financed, and the monthly mortgage payment (showing
how to apply the appropriate financial formula and showing the calculations).
Task 3: Compute the monthly amount of real estate taxes and add to the monthly mortgage payment to
get the total monthly amount paid. [Real estate taxes are typically assessed annually by the jurisdiction where
the property is located. The taxes are usually collected by the mortgage lender along with the monthly mortgage
payment.]
Task 4: Suppose that in order to qualify for the loan, the total monthly amount paid cannot exceed 30
percent of monthly income. What is the minimum monthly income needed to qualify for the loan?
What is the minimum annual income needed? (Note: This is a simplified minimum income requirement
calculation, for the purposes of this project, as it does not take into account other costs such as insurance or other
loans or assets currently held. The idea is this: Before granting a mortgage, the lender wants to be reasonably sure
that the borrower can afford the home, and a typical benchmark is that the total monthly amount paid, including real
estate taxes, does not exceed 30% of monthly income.)
Task 5: Construct an amortization table for the mortgage (using spreadsheet software or online
resources such as http://www.bankrate.com/calculators/mortgages/mortgage-calculator.aspx). Note that
the monthly mortgage payment in the amortization table should match the value you calculated in task 2.
Task 6: Referring to your amortization table, state the month and year of the first payment. Find the date
of the first month when the amount applied to the principal exceeds the amount of interest paid.
How many of the 360 payments have been made at this point?
Task 7: Calculate the unpaid balance after 22 years, rounded to the nearest dollar (showing how to
apply the appropriate financial formula and showing the calculations). What percentage of the amount
financed is still unpaid? Note: You should check your answer for the unpaid balance by consulting your
amortization table, but you must show how to calculate the value in your project.
Task 8: Assuming that the mortgage is held for the full 30 years, compute the total principal paid and
the total interest paid.
Task 9: Conclusion: Write a summary describing the results, particularly those you found to be most
interesting, and why. Do NOT just “parrot” the summary in the sample loan project. I want to read
your thoughts, not mine!
Submit your completed loan project in your WebTycho assignment folder by the end of Week 4,
February 10. Your project must include
• name of project and your name
• house’s description, asking price, and real estate taxes, the purchase price, and the current
market interest rate (include references)
• computations and answers for tasks 2, 3, and 4, amortization table for task 5, answers for task 6,
and computations and answers for tasks 7 and 8
• task 9 (conclusion)
The project is graded on the basis of 100 points.
EXTRA CREDIT (Optional, can earn up to 10 points)
For extra credit, work on one or two additional scenarios described below, carrying out steps (1), (2), (3) :
Scenario: Smaller down payment. Suppose the down payment is just 10% of the purchase price rather
than 20%.
(1) Show how to find the monthly payment (assuming a 30-year mortgage with the same interest
rate as before).
and/or
Scenario: Shorter term. Suppose the loan is a 15-year fixed rate mortgage rather than 30 years.
(1) Show how to find the monthly payment (assuming a 20% down payment with the same interest
rate as before).
(2) Make a table to compare the results of your scenario(s) with the results for your original loan
calculation. (See the Sample Loan Project for details.)
(3) In your conclusion, be sure to describe in words what you find striking in comparing the results of the
scenario(s) with the original loan results.
AMORTIZATIONTABLE: Loan Amount $310,720, Interest rate 4.625%, 30 year fixed rate mortgage
(Created by using a mortgage calculator at http://www.bankrate.com , copying and pasting the result into an Excel spreadsheet,
number the payments, shrinking the font, and pasting into a Word document.)
[Note: This sample project was created a while ago —
I chose a loan date of December, 2008, so that the first payment would be in January, 2009.]
Scroll down to January, 2024 (181st payment) to see the first month where the principal paid exceeds the interest paid.
Month /
Year Payment
Principal Interest Total
Balance # Paid Paid Interest
1 Jan. 2009 $1,597.53 $399.97 $1,197.57 $1,197.57 $310,320.03
2 Feb. 2009 $1,597.53 $401.51 $1,196.03 $2,393.59 $309,918.52
3 Mar. 2009 $1,597.53 $403.06 $1,194.48 $3,588.07 $309,515.47
4 Apr-09 $1,597.53 $404.61 $1,192.92 $4,780.99 $309,110.86
5 May-09 $1,597.53 $406.17 $1,191.36 $5,972.36 $308,704.69
6 Jun-09 $1,597.53 $407.73 $1,189.80 $7,162.16 $308,296.95
7 Jul-09 $1,597.53 $409.31 $1,188.23 $8,350.39 $307,887.65
8 Aug. 2009 $1,597.53 $410.88 $1,186.65 $9,537.04 $307,476.76
9 Sept. 2009 $1,597.53 $412.47 $1,185.07 $10,722.10 $307,064.29
10 Oct. 2009 $1,597.53 $414.06 $1,183.48 $11,905.58 $306,650.24
11 Nov. 2009 $1,597.53 $415.65 $1,181.88 $13,087.46 $306,234.58
12 Dec. 2009 $1,597.53 $417.26 $1,180.28 $14,267.74 $305,817.33
13 Jan. 2010 $1,597.53 $418.86 $1,178.67 $15,446.41 $305,398.46
14 Feb. 2010 $1,597.53 $420.48 $1,177.06 $16,623.47 $304,977.99
15 Mar. 2010 $1,597.53 $422.10 $1,175.44 $17,798.90 $304,555.89
16 Apr-10 $1,597.53 $423.73 $1,173.81 $18,972.71 $304,132.16
17 May-10 $1,597.53 $425.36 $1,172.18 $20,144.89 $303,706.81
18 Jun-10 $1,597.53 $427.00 $1,170.54 $21,315.43 $303,279.81
19 Jul-10 $1,597.53 $428.64 $1,168.89 $22,484.32 $302,851.16
20 Aug. 2010 $1,597.53 $430.30 $1,167.24 $23,651.55 $302,420.87
21 Sept. 2010 $1,597.53 $431.95 $1,165.58 $24,817.14 $301,988.91
22 Oct. 2010 $1,597.53 $433.62 $1,163.92 $25,981.05 $301,555.30
23 Nov. 2010 $1,597.53 $435.29 $1,162.24 $27,143.30 $301,120.01
24 Dec. 2010 $1,597.53 $436.97 $1,160.57 $28,303.86 $300,683.04
25 Jan. 2011 $1,597.53 $438.65 $1,158.88 $29,462.74 $300,244.39
26 Feb. 2011 $1,597.53 $440.34 $1,157.19 $30,619.94 $299,804.04
27 Mar. 2011 $1,597.53 $442.04 $1,155.49 $31,775.43 $299,362.00
28 Apr-11 $1,597.53 $443.74 $1,153.79 $32,929.22 $298,918.26
29 May-11 $1,597.53 $445.45 $1,152.08 $34,081.30 $298,472.81
30 Jun-11 $1,597.53 $447.17 $1,150.36 $35,231.67 $298,025.64
31 Jul-11 $1,597.53 $448.89 $1,148.64 $36,380.31 $297,576.74
32 Aug. 2011 $1,597.53 $450.62 $1,146.91 $37,527.22 $297,126.12
33 Sept. 2011 $1,597.53 $452.36 $1,145.17 $38,672.39 $296,673.76
34 Oct. 2011 $1,597.53 $454.10 $1,143.43 $39,815.82 $296,219.66
35 Nov. 2011 $1,597.53 $455.85 $1,141.68 $40,957.50 $295,763.80
36 Dec. 2011 $1,597.53 $457.61 $1,139.92 $42,097.42 $295,306.19
37 Jan. 2012 $1,597.53 $459.38 $1,138.16 $43,235.58 $294,846.81
38 Feb. 2012 $1,597.53 $461.15 $1,136.39 $44,371.97 $294,385.67
39 Mar. 2012 $1,597.53 $462.92 $1,134.61 $45,506.58 $293,922.75
40 Apr-12 $1,597.53 $464.71 $1,132.83 $46,639.41 $293,458.04
41 May-12 $1,597.53 $466.50 $1,131.04 $47,770.45 $292,991.54
42 Jun-12 $1,597.53 $468.30 $1,129.24 $48,899.69 $292,523.24
43 Jul-12 $1,597.53 $470.10 $1,127.43 $50,027.12 $292,053.14
44 Aug. 2012 $1,597.53 $471.91 $1,125.62 $51,152.74 $291,581.23
45 Sept. 2012 $1,597.53 $473.73 $1,123.80 $52,276.54 $291,107.50
46 Oct. 2012 $1,597.53 $475.56 $1,121.98 $53,398.52 $290,631.94
47 Nov. 2012 $1,597.53 $477.39 $1,120.14 $54,518.66 $290,154.55
48 Dec. 2012 $1,597.53 $479.23 $1,118.30 $55,636.97 $289,675.32
49 Jan. 2013 $1,597.53 $481.08 $1,116.46 $56,753.42 $289,194.24
50 Feb. 2013 $1,597.53 $482.93 $1,114.60 $57,868.03 $288,711.31
51 Mar. 2013 $1,597.53 $484.79 $1,112.74 $58,980.77 $288,226.52
52 Apr-13 $1,597.53 $486.66 $1,110.87 $60,091.64 $287,739.86
53 May-13 $1,597.53 $488.54 $1,109.00 $61,200.64 $287,251.32
54 Jun-13 $1,597.53 $490.42 $1,107.11 $62,307.75 $286,760.90
55 Jul-13 $1,597.53 $492.31 $1,105.22 $63,412.98 $286,268.59
56 Aug. 2013 $1,597.53 $494.21 $1,103.33 $64,516.31 $285,774.38
57 Sept. 2013 $1,597.53 $496.11 $1,101.42 $65,617.73 $285,278.27
58 Oct. 2013 $1,597.53 $498.02 $1,099.51 $66,717.24 $284,780.25
59 Nov. 2013 $1,597.53 $499.94 $1,097.59 $67,814.83 $284,280.30
60 Dec. 2013 $1,597.53 $501.87 $1,095.66 $68,910.49 $283,778.43
61 Jan. 2014 $1,597.53 $503.80 $1,093.73 $70,004.22 $283,274.63
62 Feb. 2014 $1,597.53 $505.75 $1,091.79 $71,096.01 $282,768.88
63 Mar. 2014 $1,597.53 $507.70 $1,089.84 $72,185.85 $282,261.19
64 Apr-14 $1,597.53 $509.65 $1,087.88 $73,273.73 $281,751.53
65 May-14 $1,597.53 $511.62 $1,085.92 $74,359.65 $281,239.92
66 Jun-14 $1,597.53 $513.59 $1,083.95 $75,443.59 $280,726.33
67 Jul-14 $1,597.53 $515.57 $1,081.97 $76,525.56 $280,210.76
68 Aug. 2014 $1,597.53 $517.56 $1,079.98 $77,605.54 $279,693.20
69 Sept. 2014 $1,597.53 $519.55 $1,077.98 $78,683.52 $279,173.65
70 Oct. 2014 $1,597.53 $521.55 $1,075.98 $79,759.50 $278,652.10
71 Nov. 2014 $1,597.53 $523.56 $1,073.97 $80,833.47 $278,128.54
72 Dec. 2014 $1,597.53 $525.58 $1,071.95 $81,905.43 $277,602.96
73 Jan. 2015 $1,597.53 $527.61 $1,069.93 $82,975.36 $277,075.35
74 Feb. 2015 $1,597.53 $529.64 $1,067.89 $84,043.25 $276,545.71
75 Mar. 2015 $1,597.53 $531.68 $1,065.85 $85,109.10 $276,014.03
76 Apr-15 $1,597.53 $533.73 $1,063.80 $86,172.91 $275,480.30
77 May-15 $1,597.53 $535.79 $1,061.75 $87,234.65 $274,944.51
78 Jun-15 $1,597.53 $537.85 $1,059.68 $88,294.34 $274,406.66
79 Jul-15 $1,597.53 $539.93 $1,057.61 $89,351.95 $273,866.74
80 Aug. 2015 $1,597.53 $542.01 $1,055.53 $90,407.47 $273,324.73
81 Sept. 2015 $1,597.53 $544.10 $1,053.44 $91,460.91 $272,780.63
82 Oct. 2015 $1,597.53 $546.19 $1,051.34 $92,512.26 $272,234.44
83 Nov. 2015 $1,597.53 $548.30 $1,049.24 $93,561.49 $271,686.14
84 Dec. 2015 $1,597.53 $550.41 $1,047.12 $94,608.62 $271,135.73
85 Jan. 2016 $1,597.53 $552.53 $1,045.00 $95,653.62 $270,583.20
86 Feb. 2016 $1,597.53 $554.66 $1,042.87 $96,696.49 $270,028.54
87 Mar. 2016 $1,597.53 $556.80 $1,040.73 $97,737.23 $269,471.74
88 Apr-16 $1,597.53 $558.95 $1,038.59 $98,775.81 $268,912.80
89 May-16 $1,597.53 $561.10 $1,036.43 $99,812.25 $268,351.70
90 Jun-16 $1,597.53 $563.26 $1,034.27 $100,846.52 $267,788.43
91 Jul-16 $1,597.53 $565.43 $1,032.10 $101,878.62 $267,223.00
92 Aug. 2016 $1,597.53 $567.61 $1,029.92 $102,908.54 $266,655.39
93 Sept. 2016 $1,597.53 $569.80 $1,027.73 $103,936.28 $266,085.59
94 Oct. 2016 $1,597.53 $572.00 $1,025.54 $104,961.82 $265,513.59
95 Nov. 2016 $1,597.53 $574.20 $1,023.33 $105,985.15 $264,939.39
96 Dec. 2016 $1,597.53 $576.41 $1,021.12 $107,006.27 $264,362.98
97 Jan. 2017 $1,597.53 $578.64 $1,018.90 $108,025.17 $263,784.34
98 Feb. 2017 $1,597.53 $580.87 $1,016.67 $109,041.84 $263,203.48
99 Mar. 2017 $1,597.53 $583.10 $1,014.43 $110,056.27 $262,620.37
100 Apr-17 $1,597.53 $585.35 $1,012.18 $111,068.45 $262,035.02
101 May-17 $1,597.53 $587.61 $1,009.93 $112,078.38 $261,447.41
102 Jun-17 $1,597.53 $589.87 $1,007.66 $113,086.04 $260,857.54
103 Jul-17 $1,597.53 $592.15 $1,005.39 $114,091.43 $260,265.40
104 Aug. 2017 $1,597.53 $594.43 $1,003.11 $115,094.54 $259,670.97
105 Sept. 2017 $1,597.53 $596.72 $1,000.82 $116,095.35 $259,074.25
106 Oct. 2017 $1,597.53 $599.02 $998.52 $117,093.87 $258,475.23
107 Nov. 2017 $1,597.53 $601.33 $996.21 $118,090.07 $257,873.90
108 Dec. 2017 $1,597.53 $603.65 $993.89 $119,083.96 $257,270.26
109 Jan. 2018 $1,597.53 $605.97 $991.56 $120,075.52 $256,664.28
110 Feb. 2018 $1,597.53 $608.31 $989.23 $121,064.75 $256,055.98
111 Mar. 2018 $1,597.53 $610.65 $986.88 $122,051.63 $255,445.33
112 Apr-18 $1,597.53 $613.01 $984.53 $123,036.16 $254,832.32
113 May-18 $1,597.53 $615.37 $982.17 $124,018.33 $254,216.95
114 Jun-18 $1,597.53 $617.74 $979.79 $124,998.12 $253,599.21
115 Jul-18 $1,597.53 $620.12 $977.41 $125,975.54 $252,979.09
116 Aug. 2018 $1,597.53 $622.51 $975.02 $126,950.56 $252,356.58
117 Sept. 2018 $1,597.53 $624.91 $972.62 $127,923.18 $251,731.67
118 Oct. 2018 $1,597.53 $627.32 $970.22 $128,893.40 $251,104.35
119 Nov. 2018 $1,597.53 $629.74 $967.80 $129,861.20 $250,474.62
120 Dec. 2018 $1,597.53 $632.16 $965.37 $130,826.57 $249,842.45
121 Jan. 2019 $1,597.53 $634.60 $962.93 $131,789.50 $249,207.85
122 Feb. 2019 $1,597.53 $637.05 $960.49 $132,749.99 $248,570.81
123 Mar. 2019 $1,597.53 $639.50 $958.03 $133,708.03 $247,931.31
124 Apr-19 $1,597.53 $641.97 $955.57 $134,663.59 $247,289.34
125 May-19 $1,597.53 $644.44 $953.09 $135,616.69 $246,644.90
126 Jun-19 $1,597.53 $646.92 $950.61 $136,567.30 $245,997.98
127 Jul-19 $1,597.53 $649.42 $948.12 $137,515.42 $245,348.56
128 Aug. 2019 $1,597.53 $651.92 $945.61 $138,461.03 $244,696.64
129 Sept. 2019 $1,597.53 $654.43 $943.10 $139,404.13 $244,042.21
130 Oct. 2019 $1,597.53 $656.95 $940.58 $140,344.71 $243,385.25
131 Nov. 2019 $1,597.53 $659.49 $938.05 $141,282.76 $242,725.76
132 Dec. 2019 $1,597.53 $662.03 $935.51 $142,218.26 $242,063.74
133 Jan. 2020 $1,597.53 $664.58 $932.95 $143,151.22 $241,399.16
134 Feb. 2020 $1,597.53 $667.14 $930.39 $144,081.61 $240,732.01
135 Mar. 2020 $1,597.53 $669.71 $927.82 $145,009.43 $240,062.30
136 Apr-20 $1,597.53 $672.29 $925.24 $145,934.67 $239,390.01
137 May-20 $1,597.53 $674.89 $922.65 $146,857.32 $238,715.12
138 Jun-20 $1,597.53 $677.49 $920.05 $147,777.37 $238,037.64
139 Jul-20 $1,597.53 $680.10 $917.44 $148,694.81 $237,357.54
140 Aug. 2020 $1,597.53 $682.72 $914.82 $149,609.62 $236,674.82
141 Sept. 2020 $1,597.53 $685.35 $912.18 $150,521.81 $235,989.47
142 Oct. 2020 $1,597.53 $687.99 $909.54 $151,431.35 $235,301.48
143 Nov. 2020 $1,597.53 $690.64 $906.89 $152,338.24 $234,610.83
144 Dec. 2020 $1,597.53 $693.31 $904.23 $153,242.47 $233,917.53
145 Jan. 2021 $1,597.53 $695.98 $901.56 $154,144.03 $233,221.55
146 Feb. 2021 $1,597.53 $698.66 $898.87 $155,042.90 $232,522.89
147 Mar. 2021 $1,597.53 $701.35 $896.18 $155,939.08 $231,821.54
148 Apr-21 $1,597.53 $704.06 $893.48 $156,832.56 $231,117.48
149 May-21 $1,597.53 $706.77 $890.77 $157,723.33 $230,410.72
150 Jun-21 $1,597.53 $709.49 $888.04 $158,611.37 $229,701.22
151 Jul-21 $1,597.53 $712.23 $885.31 $159,496.67 $228,988.99
152 Aug. 2021 $1,597.53 $714.97 $882.56 $160,379.24 $228,274.02
153 Sept. 2021 $1,597.53 $717.73 $879.81 $161,259.04 $227,556.29
154 Oct. 2021 $1,597.53 $720.49 $877.04 $162,136.08 $226,835.80
155 Nov. 2021 $1,597.53 $723.27 $874.26 $163,010.35 $226,112.53
156 Dec. 2021 $1,597.53 $726.06 $871.48 $163,881.82 $225,386.47
157 Jan. 2022 $1,597.53 $728.86 $868.68 $164,750.50 $224,657.61
158 Feb. 2022 $1,597.53 $731.67 $865.87 $165,616.37 $223,925.95
159 Mar. 2022 $1,597.53 $734.49 $863.05 $166,479.41 $223,191.46
160 Apr-22 $1,597.53 $737.32 $860.22 $167,339.63 $222,454.14
161 May-22 $1,597.53 $740.16 $857.38 $168,197.01 $221,713.98
162 Jun-22 $1,597.53 $743.01 $854.52 $169,051.53 $220,970.97
163 Jul-22 $1,597.53 $745.88 $851.66 $169,903.19 $220,225.10
164 Aug. 2022 $1,597.53 $748.75 $848.78 $170,751.97 $219,476.35
165 Sept. 2022 $1,597.53 $751.64 $845.90 $171,597.87 $218,724.71
166 Oct. 2022 $1,597.53 $754.53 $843.00 $172,440.87 $217,970.18
167 Nov. 2022 $1,597.53 $757.44 $840.09 $173,280.97 $217,212.74
168 Dec. 2022 $1,597.53 $760.36 $837.17 $174,118.14 $216,452.38
169 Jan. 2023 $1,597.53 $763.29 $834.24 $174,952.38 $215,689.09
170 Feb. 2023 $1,597.53 $766.23 $831.30 $175,783.68 $214,922.85
171 Mar. 2023 $1,597.53 $769.19 $828.35 $176,612.03 $214,153.67
172 Apr-23 $1,597.53 $772.15 $825.38 $177,437.42 $213,381.52
173 May-23 $1,597.53 $775.13 $822.41 $178,259.82 $212,606.39
174 Jun-23 $1,597.53 $778.11 $819.42 $179,079.25 $211,828.28
175 Jul-23 $1,597.53 $781.11 $816.42 $179,895.67 $211,047.16
176 Aug. 2023 $1,597.53 $784.12 $813.41 $180,709.08 $210,263.04
177 Sept. 2023 $1,597.53 $787.15 $810.39 $181,519.47 $209,475.89
178 Oct. 2023 $1,597.53 $790.18 $807.36 $182,326.82 $208,685.72
179 Nov. 2023 $1,597.53 $793.22 $804.31 $183,131.13 $207,892.49
180 Dec. 2023 $1,597.53 $796.28 $801.25 $183,932.38 $207,096.21
181 Jan. 2024 $1,597.53 $799.35 $798.18 $184,730.57 $206,296.86
182 Feb. 2024 $1,597.53 $802.43 $795.10 $185,525.67 $205,494.43
183 Mar. 2024 $1,597.53 $805.52 $792.01 $186,317.68 $204,688.90
184 Apr-24 $1,597.53 $808.63 $788.91 $187,106.58 $203,880.27
185 May-24 $1,597.53 $811.75 $785.79 $187,892.37 $203,068.53
186 Jun-24 $1,597.53 $814.87 $782.66 $188,675.03 $202,253.65
187 Jul-24 $1,597.53 $818.02 $779.52 $189,454.55 $201,435.64
188 Aug. 2024 $1,597.53 $821.17 $776.37 $190,230.92 $200,614.47
189 Sept. 2024 $1,597.53 $824.33 $773.20 $191,004.12 $199,790.14
190 Oct. 2024 $1,597.53 $827.51 $770.02 $191,774.14 $198,962.63
191 Nov. 2024 $1,597.53 $830.70 $766.84 $192,540.98 $198,131.93
192 Dec. 2024 $1,597.53 $833.90 $763.63 $193,304.61 $197,298.03
193 Jan. 2025 $1,597.53 $837.11 $760.42 $194,065.03 $196,460.91
194 Feb. 2025 $1,597.53 $840.34 $757.19 $194,822.23 $195,620.57
195 Mar. 2025 $1,597.53 $843.58 $753.95 $195,576.18 $194,776.99
196 Apr-25 $1,597.53 $846.83 $750.70 $196,326.88 $193,930.16
197 May-25 $1,597.53 $850.10 $747.44 $197,074.32 $193,080.06
198 Jun-25 $1,597.53 $853.37 $744.16 $197,818.48 $192,226.69
199 Jul-25 $1,597.53 $856.66 $740.87 $198,559.36 $191,370.03
200 Aug. 2025 $1,597.53 $859.96 $737.57 $199,296.93 $190,510.07
201 Sept. 2025 $1,597.53 $863.28 $734.26 $200,031.19 $189,646.79
202 Oct. 2025 $1,597.53 $866.60 $730.93 $200,762.12 $188,780.19
203 Nov. 2025 $1,597.53 $869.94 $727.59 $201,489.71 $187,910.24
204 Dec. 2025 $1,597.53 $873.30 $724.24 $202,213.95 $187,036.95
205 Jan. 2026 $1,597.53 $876.66 $720.87 $202,934.82 $186,160.29
206 Feb. 2026 $1,597.53 $880.04 $717.49 $203,652.31 $185,280.24
207 Mar. 2026 $1,597.53 $883.43 $714.10 $204,366.41 $184,396.81
208 Apr-26 $1,597.53 $886.84 $710.70 $205,077.11 $183,509.97
209 May-26 $1,597.53 $890.26 $707.28 $205,784.39 $182,619.72
210 Jun-26 $1,597.53 $893.69 $703.85 $206,488.23 $181,726.03
211 Jul-26 $1,597.53 $897.13 $700.40 $207,188.63 $180,828.90
212 Aug. 2026 $1,597.53 $900.59 $696.94 $207,885.58 $179,928.31
213 Sept. 2026 $1,597.53 $904.06 $693.47 $208,579.05 $179,024.25
214 Oct. 2026 $1,597.53 $907.55 $689.99 $209,269.04 $178,116.70
215 Nov. 2026 $1,597.53 $911.04 $686.49 $209,955.53 $177,205.66
216 Dec. 2026 $1,597.53 $914.55 $682.98 $210,638.51 $176,291.10
217 Jan. 2027 $1,597.53 $918.08 $679.46 $211,317.97 $175,373.03
218 Feb. 2027 $1,597.53 $921.62 $675.92 $211,993.89 $174,451.41
219 Mar. 2027 $1,597.53 $925.17 $672.36 $212,666.25 $173,526.24
220 Apr-27 $1,597.53 $928.74 $668.80 $213,335.05 $172,597.50
221 May-27 $1,597.53 $932.31 $665.22 $214,000.27 $171,665.19
222 Jun-27 $1,597.53 $935.91 $661.63 $214,661.90 $170,729.28
223 Jul-27 $1,597.53 $939.52 $658.02 $215,319.91 $169,789.76
224 Aug. 2027 $1,597.53 $943.14 $654.40 $215,974.31 $168,846.63
225 Sept. 2027 $1,597.53 $946.77 $650.76 $216,625.08 $167,899.86
226 Oct. 2027 $1,597.53 $950.42 $647.11 $217,272.19 $166,949.44
227 Nov. 2027 $1,597.53 $954.08 $643.45 $217,915.64 $165,995.35
228 Dec. 2027 $1,597.53 $957.76 $639.77 $218,555.41 $165,037.59
229 Jan. 2028 $1,597.53 $961.45 $636.08 $219,191.50 $164,076.14
230 Feb. 2028 $1,597.53 $965.16 $632.38 $219,823.87 $163,110.98
231 Mar. 2028 $1,597.53 $968.88 $628.66 $220,452.53 $162,142.11
232 Apr-28 $1,597.53 $972.61 $624.92 $221,077.45 $161,169.49
233 May-28 $1,597.53 $976.36 $621.17 $221,698.63 $160,193.13
234 Jun-28 $1,597.53 $980.12 $617.41 $222,316.04 $159,213.01
235 Jul-28 $1,597.53 $983.90 $613.63 $222,929.67 $158,229.11
236 Aug. 2028 $1,597.53 $987.69 $609.84 $223,539.51 $157,241.42
237 Sept. 2028 $1,597.53 $991.50 $606.03 $224,145.55 $156,249.92
238 Oct. 2028 $1,597.53 $995.32 $602.21 $224,747.76 $155,254.60
239 Nov. 2028 $1,597.53 $999.16 $598.38 $225,346.14 $154,255.44
240 Dec. 2028 $1,597.53 $1,003.01 $594.53 $225,940.66 $153,252.43
241 Jan. 2029 $1,597.53 $1,006.87 $590.66 $226,531.32 $152,245.56
242 Feb. 2029 $1,597.53 $1,010.75 $586.78 $227,118.10 $151,234.80
243 Mar. 2029 $1,597.53 $1,014.65 $582.88 $227,700.99 $150,220.15
244 Apr-29 $1,597.53 $1,018.56 $578.97 $228,279.96 $149,201.59
245 May-29 $1,597.53 $1,022.49 $575.05 $228,855.01 $148,179.11
246 Jun-29 $1,597.53 $1,026.43 $571.11 $229,426.12 $147,152.68
247 Jul-29 $1,597.53 $1,030.38 $567.15 $229,993.27 $146,122.29
248 Aug. 2029 $1,597.53 $1,034.35 $563.18 $230,556.45 $145,087.94
249 Sept. 2029 $1,597.53 $1,038.34 $559.19 $231,115.64 $144,049.60
250 Oct. 2029 $1,597.53 $1,042.34 $555.19 $231,670.83 $143,007.26
251 Nov. 2029 $1,597.53 $1,046.36 $551.17 $232,222.01 $141,960.90
252 Dec. 2029 $1,597.53 $1,050.39 $547.14 $232,769.15 $140,910.50
253 Jan. 2030 $1,597.53 $1,054.44 $543.09 $233,312.24 $139,856.06
254 Feb. 2030 $1,597.53 $1,058.51 $539.03 $233,851.27 $138,797.55
255 Mar. 2030 $1,597.53 $1,062.59 $534.95 $234,386.22 $137,734.97
256 Apr-30 $1,597.53 $1,066.68 $530.85 $234,917.07 $136,668.29
257 May-30 $1,597.53 $1,070.79 $526.74 $235,443.81 $135,597.50
258 Jun-30 $1,597.53 $1,074.92 $522.62 $235,966.43 $134,522.58
259 Jul-30 $1,597.53 $1,079.06 $518.47 $236,484.90 $133,443.52
260 Aug. 2030 $1,597.53 $1,083.22 $514.31 $236,999.21 $132,360.29
261 Sept. 2030 $1,597.53 $1,087.40 $510.14 $237,509.35 $131,272.90
262 Oct. 2030 $1,597.53 $1,091.59 $505.95 $238,015.30 $130,181.31
263 Nov. 2030 $1,597.53 $1,095.79 $501.74 $238,517.04 $129,085.52
264 Dec. 2030 $1,597.53 $1,100.02 $497.52 $239,014.56 $127,985.50
265 Jan. 2031 $1,597.53 $1,104.26 $493.28 $239,507.84 $126,881.24
266 Feb. 2031 $1,597.53 $1,108.51 $489.02 $239,996.86 $125,772.73
267 Mar. 2031 $1,597.53 $1,112.79 $484.75 $240,481.61 $124,659.95
268 Apr-31 $1,597.53 $1,117.07 $480.46 $240,962.07 $123,542.87
269 May-31 $1,597.53 $1,121.38 $476.15 $241,438.22 $122,421.49
270 Jun-31 $1,597.53 $1,125.70 $471.83 $241,910.05 $121,295.79
271 Jul-31 $1,597.53 $1,130.04 $467.49 $242,377.55 $120,165.75
272 Aug. 2031 $1,597.53 $1,134.40 $463.14 $242,840.69 $119,031.36
273 Sept. 2031 $1,597.53 $1,138.77 $458.77 $243,299.45 $117,892.59
274 Oct. 2031 $1,597.53 $1,143.16 $454.38 $243,753.83 $116,749.43
275 Nov. 2031 $1,597.53 $1,147.56 $449.97 $244,203.80 $115,601.87
276 Dec. 2031 $1,597.53 $1,151.99 $445.55 $244,649.35 $114,449.88
277 Jan. 2032 $1,597.53 $1,156.43 $441.11 $245,090.46 $113,293.46
278 Feb. 2032 $1,597.53 $1,160.88 $436.65 $245,527.11 $112,132.58
279 Mar. 2032 $1,597.53 $1,165.36 $432.18 $245,959.29 $110,967.22
280 Apr-32 $1,597.53 $1,169.85 $427.69 $246,386.98 $109,797.37
281 May-32 $1,597.53 $1,174.36 $423.18 $246,810.15 $108,623.01
282 Jun-32 $1,597.53 $1,178.88 $418.65 $247,228.80 $107,444.13
283 Jul-32 $1,597.53 $1,183.43 $414.11 $247,642.91 $106,260.70
284 Aug. 2032 $1,597.53 $1,187.99 $409.55 $248,052.46 $105,072.72
285 Sept. 2032 $1,597.53 $1,192.57 $404.97 $248,457.43 $103,880.15
286 Oct. 2032 $1,597.53 $1,197.16 $400.37 $248,857.80 $102,682.99
287 Nov. 2032 $1,597.53 $1,201.78 $395.76 $249,253.56 $101,481.21
288 Dec. 2032 $1,597.53 $1,206.41 $391.13 $249,644.68 $100,274.80
289 Jan. 2033 $1,597.53 $1,211.06 $386.48 $250,031.16 $99,063.74
290 Feb. 2033 $1,597.53 $1,215.73 $381.81 $250,412.96 $97,848.02
291 Mar. 2033 $1,597.53 $1,220.41 $377.12 $250,790.09 $96,627.61
292 Apr-33 $1,597.53 $1,225.12 $372.42 $251,162.51 $95,402.49
293 May-33 $1,597.53 $1,229.84 $367.70 $251,530.20 $94,172.65
294 Jun-33 $1,597.53 $1,234.58 $362.96 $251,893.16 $92,938.08
295 Jul-33 $1,597.53 $1,239.34 $358.20 $252,251.36 $91,698.74
296 Aug. 2033 $1,597.53 $1,244.11 $353.42 $252,604.78 $90,454.63
297 Sept. 2033 $1,597.53 $1,248.91 $348.63 $252,953.41 $89,205.72
298 Oct. 2033 $1,597.53 $1,253.72 $343.81 $253,297.22 $87,952.00
299 Nov. 2033 $1,597.53 $1,258.55 $338.98 $253,636.20 $86,693.45
300 Dec. 2033 $1,597.53 $1,263.40 $334.13 $253,970.34 $85,430.04
301 Jan. 2034 $1,597.53 $1,268.27 $329.26 $254,299.60 $84,161.77
302 Feb. 2034 $1,597.53 $1,273.16 $324.37 $254,623.97 $82,888.61
303 Mar. 2034 $1,597.53 $1,278.07 $319.47 $254,943.44 $81,610.54
304 Apr-34 $1,597.53 $1,282.99 $314.54 $255,257.98 $80,327.55
305 May-34 $1,597.53 $1,287.94 $309.60 $255,567.57 $79,039.61
306 Jun-34 $1,597.53 $1,292.90 $304.63 $255,872.21 $77,746.71
307 Jul-34 $1,597.53 $1,297.89 $299.65 $256,171.85 $76,448.82
308 Aug. 2034 $1,597.53 $1,302.89 $294.65 $256,466.50 $75,145.93
309 Sept. 2034 $1,597.53 $1,307.91 $289.62 $256,756.13 $73,838.03
310 Oct. 2034 $1,597.53 $1,312.95 $284.58 $257,040.71 $72,525.08
311 Nov. 2034 $1,597.53 $1,318.01 $279.52 $257,320.23 $71,207.06
312 Dec. 2034 $1,597.53 $1,323.09 $274.44 $257,594.68 $69,883.97
313 Jan. 2035 $1,597.53 $1,328.19 $269.34 $257,864.02 $68,555.78
314 Feb. 2035 $1,597.53 $1,333.31 $264.23 $258,128.25 $67,222.48
315 Mar. 2035 $1,597.53 $1,338.45 $259.09 $258,387.33 $65,884.03
316 Apr-35 $1,597.53 $1,343.61 $253.93 $258,641.26 $64,540.42
317 May-35 $1,597.53 $1,348.78 $248.75 $258,890.01 $63,191.64
318 Jun-35 $1,597.53 $1,353.98 $243.55 $259,133.56 $61,837.65
319 Jul-35 $1,597.53 $1,359.20 $238.33 $259,371.89 $60,478.45
320 Aug. 2035 $1,597.53 $1,364.44 $233.09 $259,604.99 $59,114.01
321 Sept. 2035 $1,597.53 $1,369.70 $227.84 $259,832.82 $57,744.31
322 Oct. 2035 $1,597.53 $1,374.98 $222.56 $260,055.38 $56,369.33
323 Nov. 2035 $1,597.53 $1,380.28 $217.26 $260,272.64 $54,989.06
324 Dec. 2035 $1,597.53 $1,385.60 $211.94 $260,484.57 $53,603.46
325 Jan. 2036 $1,597.53 $1,390.94 $206.60 $260,691.17 $52,212.52
326 Feb. 2036 $1,597.53 $1,396.30 $201.24 $260,892.41 $50,816.22
327 Mar. 2036 $1,597.53 $1,401.68 $195.85 $261,088.26 $49,414.54
328 Apr-36 $1,597.53 $1,407.08 $190.45 $261,278.71 $48,007.46
329 May-36 $1,597.53 $1,412.51 $185.03 $261,463.74 $46,594.96
330 Jun-36 $1,597.53 $1,417.95 $179.58 $261,643.33 $45,177.01
331 Jul-36 $1,597.53 $1,423.41 $174.12 $261,817.45 $43,753.59
332 Aug. 2036 $1,597.53 $1,428.90 $168.63 $261,986.08 $42,324.69
333 Sept. 2036 $1,597.53 $1,434.41 $163.13 $262,149.21 $40,890.28
334 Oct. 2036 $1,597.53 $1,439.94 $157.60 $262,306.80 $39,450.35
335 Nov. 2036 $1,597.53 $1,445.49 $152.05 $262,458.85 $38,004.86
336 Dec. 2036 $1,597.53 $1,451.06 $146.48 $262,605.33 $36,553.80
337 Jan. 2037 $1,597.53 $1,456.65 $140.88 $262,746.21 $35,097.15
338 Feb. 2037 $1,597.53 $1,462.26 $135.27 $262,881.48 $33,634.89
339 Mar. 2037 $1,597.53 $1,467.90 $129.63 $263,011.12 $32,166.99
340 Apr-37 $1,597.53 $1,473.56 $123.98 $263,135.10 $30,693.43
341 May-37 $1,597.53 $1,479.24 $118.30 $263,253.39 $29,214.20
342 Jun-37 $1,597.53 $1,484.94 $112.60 $263,365.99 $27,729.26
343 Jul-37 $1,597.53 $1,490.66 $106.87 $263,472.86 $26,238.60
344 Aug. 2037 $1,597.53 $1,496.41 $101.13 $263,573.99 $24,742.19
345 Sept. 2037 $1,597.53 $1,502.17 $95.36 $263,669.35 $23,240.02
346 Oct. 2037 $1,597.53 $1,507.96 $89.57 $263,758.92 $21,732.05
347 Nov. 2037 $1,597.53 $1,513.78 $83.76 $263,842.68 $20,218.28
348 Dec. 2037 $1,597.53 $1,519.61 $77.92 $263,920.61 $18,698.67
349 Jan. 2038 $1,597.53 $1,525.47 $72.07 $263,992.67 $17,173.20
350 Feb. 2038 $1,597.53 $1,531.35 $66.19 $264,058.86 $15,641.86
351 Mar. 2038 $1,597.53 $1,537.25 $60.29 $264,119.15 $14,104.61
352 Apr-38 $1,597.53 $1,543.17 $54.36 $264,173.51 $12,561.43
353 May-38 $1,597.53 $1,549.12 $48.41 $264,221.92 $11,012.31
354 Jun-38 $1,597.53 $1,555.09 $42.44 $264,264.37 $9,457.22
355 Jul-38 $1,597.53 $1,561.08 $36.45 $264,300.82 $7,896.14
356 Aug. 2038 $1,597.53 $1,567.10 $30.43 $264,331.25 $6,329.04
357 Sept. 2038 $1,597.53 $1,573.14 $24.39 $264,355.64 $4,755.90
358 Oct. 2038 $1,597.53 $1,579.20 $18.33 $264,373.97 $3,176.69
359 Nov. 2038 $1,597.53 $1,585.29 $12.24 $264,386.22 $1,591.40
360 Dec. 2038 $1,597.53 $1,591.40 $6.13 $264,392.35 $0.00
Page 1 of 4
(Sample) Loan Project: Buying a House in Purcellville, Virginia
Submitted by Suzanne Sands
Purpose: To analyze the financial implications of purchasing a house.
Task (1): House Description:
I decided to choose a house in my hometown. This house is typical of homes in the new developments
around town. I have no interest in moving, though — I am happy in my own house, which was built in the
1970s and does not look like this house at all!)
Asking price: $439,000
Real estate taxes: $4,836 (found in the http://www.loudoun.gov property database)
Purchase Price: $388,400 (I chose this value because it was the assessed value at the time this project
was prepared, according to the county property database)
Current market interest rate (30 yr fixed rate): 4.625% through AimLoan.com (found at
http://www.bankrate.com, by doing a search for my zipcode)
[NOTE: This sample project was completed quite some time ago, so interest rates, taxes, and purchase prices could
be quite different now.]
Page 2 of 4
Task (2)
20% down payment: $77,680 (= 0.20 x $388,400)
Amount financed (i.e., amount borrowed): $310,720 (= $388,400 – 77,680)
Monthly mortgage payment: $1,597.53 (see below for details of calculation)
Payment calculation:
• present value PV = $310,720
• annual interest rate r = 0.04625
• interest compounded m = 12 times per year
• number of payments n = 30 x 12 = 360 The interest rate per month is i = r/m = 0.04625/12.
The monthly mortgage payment PMT is
��� = ��
�
�� �
���
= 310,720
�.�����/��
� � �
�.�����/�������
≈ 310,720
�.�� !����”
���.��� ���
≈ 310,720 0.005141396� = $1,597.53
Remark: Intermediate results must be computed with great precision, so that the final value has 6 digits of accuracy
(an amount involving dollars and cents, with the dollar amount in the thousands).
Task (3):
Monthly real estate taxes: $403.00 (= $4836/12)
Total monthly payment = Monthly mortgage payment + Monthly taxes = 1597.53 + 403.00 = $2000.53
The total monthly payment is used when determining the income level needed to afford the home.
Task (4): Minimum income requirement
Total monthly payment ≤ 0.30 x Monthly Income
(Total monthly payment)/0.30 ≤ Monthly Income
Monthly Income ≥ (Total monthly payment)/0.30 = $2000.53/(0.30) = $6,668.43
Annual income = 12(Monthly Income) = 12($6668.43) = $80,021.16
In order to qualify for the loan, the monthly income must be at least $6,668.43, and the annual income
must be at least $80,021.16.
Task (5): Amortization Table — See separate document (generated by using the amortization schedule
calculator at http://www.bankrate.com , pasted into a spreadsheet, and then reformatted to paste into a Word
document).
Task (6)
In this sample project, the mortgage was set up in December, 2008, with the first payment in January,
2009.
By consulting the amortization table, January, 2024 is the first month when the amount applied to the
principal ($799.35) exceeds the amount of interest ($799.18) paid. This is the 181
st
payment.
Page 3 of 4
Task (7)
After 22 years, 22(12) = 264 payments have been made, so there are 360 − 264 = 96 payments
remaining. To find the unpaid balance, calculate PV, the amount remaining to be paid off by 96 monthly
payments of $1,597.53 at an interest rate of 4.625% compounded monthly.
�� = ���
� � �
���
�
= 1,597.53
� � �
�.�����/����(�
�.�����/��
= 1,597.53
���.�)����”��
�.�� !������”
= $127,985.17
The unpaid balance after 22 years is $127,985 (rounded to the nearest dollar)
Notice that this amount agrees with the amount in the amortization table for the unpaid balance after 264
payments. (It is very close but not precisely the same as the amount in the amortization table, because in going month to month
in the table, there are issues involving repeated rounding to the nearest cent, accumulating over time.)
Since $127,985/310,720 ≈ 0.412, the unpaid amount after 22 years is 41% of the amount financed.
Note that 96/360 = 27%. When 27% of the payments are remaining, 41% of the amount financed is still owed.
Task (8) [Assuming the loan is held for the full 30 years]
Total principal paid = Amount borrowed = $310,720
Total interest paid = 360($1597.53) – $310,720 = $264,390.80
Task (9) Conclusion
For a 30-year loan of $310,720 at an interest rate of 4.625%, the monthly payment is $1,597.53, and the
borrower would need a minimum annual income of about $80,000 to qualify for the loan.
It takes a bit over 15 years to reach the point where the monthly principal applied is larger than the
monthly interest paid. After 24 years, nearly a third of the amount borrowed is still owed.
If the mortgage is held for the full 30 years, then $264,391 will be paid in interest, which is 85% of the
amount borrowed.
Without understanding a loan analysis, a common misconception is that the unpaid balance is reduced by
the same amount each year. However, interest is charged monthly on the amount owed, which is very
large at the beginning and gradually diminishes. A quick scan of the amortization table confirms that at
the start of the 30 year mortgage, almost all of the monthly payment is interest paid to the lender, and
little is applied to reducing the principal. Indeed, for the loan in this project, it takes over half of the 30 year
period before more of the monthly payment is applied to reducing the principal than in paying interest.
And, when 73% the 30 year period has elapsed, about 41% of the amount borrowed is still owed.
Extra credit:
Scenario: Smaller down payment
Suppose the down payment is just 10% of the purchase price. (Assume the loan is still a 30-year fixed
rate mortgage at the same interest rate.)
10% down payment: $38,840 (= 0.10 x $388,400)
Amount financed: $349,560 (= $388,400 – $38,840)
Monthly mortgage payment: $1,797.23 (see below for details of calculation)
Payment calculation:
• present value PV = $349,560
• annual interest rate r = 0.04625
• interest compounded m = 12 times per year
• number of payments n = 30 x 12 = 360 The interest rate per month is i = r/m = 0.04625/12.
Page 4 of 4
The monthly mortgage payment PMT is
��� = ��
�
�� �
���
= 349,560
�.�����/��
� � �
�.�����/�������
≈ 349,560
�.�� !����”
���.��� ���
≈ 349,560 0.005141396� = $1,797.23
Scenario: Shorter term
Suppose the loan is a 15-year fixed rate mortgage. (Assume the loan has the same interest rate and that
the down payment is 20% of the purchase price.)
20% down payment: $77,680 (= 0.20 x $388,400)
Amount financed: $310,720 (= $388,400 – 77,680)
Monthly mortgage payment: $2,396.89 (see below for details of calculation)
Payment calculation: .
• present value PV = $310,720
• annual interest rate r = 0.04625
• interest compounded m = 12 times per year
• number of payments n = 15 x 12 = 180 The interest rate per month is i = r/m = 0.04625/12.
The monthly mortgage payment PMT is
��� = ��
�
�� �
���
= 310,720
�.�����/��
� � �
�.�����/����+,�
≈ 310,720
�.�� !����”
���.��� ����!
≈ 310,720 0.007713972� = $2,396.89
Comparison of Mortgages
Scenario Original
(20% down, 30 years)
Smaller Down Payment
(10% down, 30 years)
Shorter Term
(15 years, 20% down)
Purchase Price $388,400 $388,400 $388,400
Down Payment $77,680 $38,840 $77,680
Amount Financed (PV) $310,720 $349,560 $310,720
Annual Interest Rate 4.625% 4.625% 4.625%
Number of Payments 360 360 180
Monthly Payment (PMT) $1,597.53 $1,797.23 $2,396.89
Total Interest Paid (If loan
held for entire term)
$264,390.80 $297,442.80 $120,720.20
Conclusion: (Drawn from extra credit scenarios)
By making a 20% down payment rather than a 10% down payment, the borrower saves about $33,000
( ≈ $297,443 – 264,391) in interest over the course of the loan. The 20% down payment also provides
more of a cushion in case real estate values decline. With a 20% down payment, a borrower is less likely
to be “underwater” later, owing more than the property is valued.
By taking out a 15-year loan of $310,720 rather than a 30-year loan, the borrower saves over $143,600
( ≈ $264,391 – 120,720) in interest over the course of the loan. For the 15-year mortgage, $120,720 will
be paid in interest, which is about 39% of the amount borrowed. However, since the monthly payment is
$2,396.89, substantially higher than for the 30-year loan, the borrower will need a higher annual income.
For this 15-year loan, the borrower would need a minimum annual income of about $112,000
[ ≈ 12(2397 + 403)/0.30] to qualify for the loan.
(Sample)Loan Project: Buying a House in Purcellville, Virginia
Submitted by Suzanne Sands
Purpose: To analyze the financial implications of purchasing a house.
Task (1): House Description:
I decided to choose a house in my hometown. This house is typical of homes in the new developments
around town. I have no interest in moving, though — I am happy in my own house, which was built in the
1970s and does not look like this house at all!)
Asking price: $439,000
Real estate taxes: $4,836 (found in the http://www.loudoun.gov property database)
Purchase Price: $388,400 (I chose this value because it was the assessed value at the time this project
was prepared, according to the county property database)
Current market interest rate (30 yr fixed rate): 4.625% through AimLoan.com (found at
http://www.bankrate.com, by doing a search for my zipcode)
[NOTE: This sample project was completed quite some time ago, so interest rates, taxes, and purchase prices could
be quite different now.]
