Question

In: Finance

You need a 30-year, fixed-rate mortgage to buy a new home for $290,000. Your mortgage bank...

You need a 30-year, fixed-rate mortgage to buy a new home for $290,000. Your mortgage bank will lend you the money at a 5.85% APR (semi-annual) for this 360-month loan. However, you can afford monthly payments of only $1,300, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,300?

Please specify what equations are used in solving

Solutions

Expert Solution

Formula:

Amortization schedule:

Number of pay out
(t)
beginning Balance
(A)
Interest
(I = A*r%)
Monthly payment
(M)
Amortisation of loan
(B) = (M)-(I)
Ending Balance
(C) = (A) -(B)
1 290000.00 1396.82 1300.00 -96.82 290096.82
2 290096.82 1397.29 1300.00 -97.29 290194.11
3 290194.11 1397.76 1300.00 -97.76 290291.87
4 290291.87 1398.23 1300.00 -98.23 290390.09
5 290390.09 1398.70 1300.00 -98.70 290488.79
6 290488.79 1399.18 1300.00 -99.18 290587.97
7 290587.97 1399.65 1300.00 -99.65 290687.62
8 290687.62 1400.13 1300.00 -100.13 290787.76
9 290787.76 1400.62 1300.00 -100.62 290888.37
10 290888.37 1401.10 1300.00 -101.10 290989.47
11 290989.47 1401.59 1300.00 -101.59 291091.06
12 291091.06 1402.08 1300.00 -102.08 291193.14
13 291193.14 1402.57 1300.00 -102.57 291295.71
14 291295.71 1403.06 1300.00 -103.06 291398.77
15 291398.77 1403.56 1300.00 -103.56 291502.33
16 291502.33 1404.06 1300.00 -104.06 291606.39
17 291606.39 1404.56 1300.00 -104.56 291710.95
18 291710.95 1405.06 1300.00 -105.06 291816.01
19 291816.01 1405.57 1300.00 -105.57 291921.58
20 291921.58 1406.08 1300.00 -106.08 292027.65
21 292027.65 1406.59 1300.00 -106.59 292134.24
22 292134.24 1407.10 1300.00 -107.10 292241.34
23 292241.34 1407.62 1300.00 -107.62 292348.96
24 292348.96 1408.14 1300.00 -108.14 292457.10
25 292457.10 1408.66 1300.00 -108.66 292565.75
26 292565.75 1409.18 1300.00 -109.18 292674.93
27 292674.93 1409.71 1300.00 -109.71 292784.64
28 292784.64 1410.23 1300.00 -110.23 292894.87
29 292894.87 1410.77 1300.00 -110.77 293005.64
30 293005.64 1411.30 1300.00 -111.30 293116.94
31 293116.94 1411.83 1300.00 -111.83 293228.77
32 293228.77 1412.37 1300.00 -112.37 293341.15
33 293341.15 1412.91 1300.00 -112.91 293454.06
34 293454.06 1413.46 1300.00 -113.46 293567.52
35 293567.52 1414.01 1300.00 -114.01 293681.52
36 293681.52 1414.55 1300.00 -114.55 293796.08
37 293796.08 1415.11 1300.00 -115.11 293911.18
38 293911.18 1415.66 1300.00 -115.66 294026.84
39 294026.84 1416.22 1300.00 -116.22 294143.06
40 294143.06 1416.78 1300.00 -116.78 294259.84
41 294259.84 1417.34 1300.00 -117.34 294377.18
42 294377.18 1417.90 1300.00 -117.90 294495.08
43 294495.08 1418.47 1300.00 -118.47 294613.56
44 294613.56 1419.04 1300.00 -119.04 294732.60
45 294732.60 1419.62 1300.00 -119.62 294852.22
46 294852.22 1420.19 1300.00 -120.19 294972.41
47 294972.41 1420.77 1300.00 -120.77 295093.18
48 295093.18 1421.35 1300.00 -121.35 295214.54
49 295214.54 1421.94 1300.00 -121.94 295336.47
50 295336.47 1422.53 1300.00 -122.53 295459.00
51 295459.00 1423.12 1300.00 -123.12 295582.12
52 295582.12 1423.71 1300.00 -123.71 295705.82
53 295705.82 1424.30 1300.00 -124.30 295830.13
54 295830.13 1424.90 1300.00 -124.90 295955.03
55 295955.03 1425.50 1300.00 -125.50 296080.54
56 296080.54 1426.11 1300.00 -126.11 296206.65
57 296206.65 1426.72 1300.00 -126.72 296333.36
58 296333.36 1427.33 1300.00 -127.33 296460.69
59 296460.69 1427.94 1300.00 -127.94 296588.63
60 296588.63 1428.56 1300.00 -128.56 296717.19
61 296717.19 1429.18 1300.00 -129.18 296846.36
62 296846.36 1429.80 1300.00 -129.80 296976.16
63 296976.16 1430.42 1300.00 -130.42 297106.58
64 297106.58 1431.05 1300.00 -131.05 297237.64
65 297237.64 1431.68 1300.00 -131.68 297369.32
66 297369.32 1432.32 1300.00 -132.32 297501.63
67 297501.63 1432.95 1300.00 -132.95 297634.59
68 297634.59 1433.59 1300.00 -133.59 297768.18
69 297768.18 1434.24 1300.00 -134.24 297902.42
70 297902.42 1434.88 1300.00 -134.88 298037.31
71 298037.31 1435.53 1300.00 -135.53 298172.84
72 298172.84 1436.19 1300.00 -136.19 298309.03
73 298309.03 1436.84 1300.00 -136.84 298445.87
74 298445.87 1437.50 1300.00 -137.50 298583.37
75 298583.37 1438.16 1300.00 -138.16 298721.54
76 298721.54 1438.83 1300.00 -138.83 298860.37
77 298860.37 1439.50 1300.00 -139.50 298999.87
78 298999.87 1440.17 1300.00 -140.17 299140.04
79 299140.04 1440.85 1300.00 -140.85 299280.88
80 299280.88 1441.52 1300.00 -141.52 299422.41
81 299422.41 1442.21 1300.00 -142.21 299564.61
82 299564.61 1442.89 1300.00 -142.89 299707.50
83 299707.50 1443.58 1300.00 -143.58 299851.08
84 299851.08 1444.27 1300.00 -144.27 299995.35
85 299995.35 1444.97 1300.00 -144.97 300140.32
86 300140.32 1445.66 1300.00 -145.66 300285.98
87 300285.98 1446.37 1300.00 -146.37 300432.35
88 300432.35 1447.07 1300.00 -147.07 300579.42
89 300579.42 1447.78 1300.00 -147.78 300727.20
90 300727.20 1448.49 1300.00 -148.49 300875.69
91 300875.69 1449.21 1300.00 -149.21 301024.89
92 301024.89 1449.92 1300.00 -149.92 301174.82
93 301174.82 1450.65 1300.00 -150.65 301325.47
94 301325.47 1451.37 1300.00 -151.37 301476.84
95 301476.84 1452.10 1300.00 -152.10 301628.94
96 301628.94 1452.83 1300.00 -152.83 301781.77
97 301781.77 1453.57 1300.00 -153.57 301935.34
98 301935.34 1454.31 1300.00 -154.31 302089.65
99 302089.65 1455.05 1300.00 -155.05 302244.71
100 302244.71 1455.80 1300.00 -155.80 302400.51
101 302400.51 1456.55 1300.00 -156.55 302557.06
102 302557.06 1457.30 1300.00 -157.30 302714.36
103 302714.36 1458.06 1300.00 -158.06 302872.42
104 302872.42 1458.82 1300.00 -158.82 303031.25
105 303031.25 1459.59 1300.00 -159.59 303190.83
106 303190.83 1460.36 1300.00 -160.36 303351.19
107 303351.19 1461.13 1300.00 -161.13 303512.32
108 303512.32 1461.91 1300.00 -161.91 303674.23
109 303674.23 1462.69 1300.00 -162.69 303836.91
110 303836.91 1463.47 1300.00 -163.47 304000.38
111 304000.38 1464.26 1300.00 -164.26 304164.64
112 304164.64 1465.05 1300.00 -165.05 304329.68
113 304329.68 1465.84 1300.00 -165.84 304495.53
114 304495.53 1466.64 1300.00 -166.64 304662.17
115 304662.17 1467.44 1300.00 -167.44 304829.61
116 304829.61 1468.25 1300.00 -168.25 304997.86
117 304997.86 1469.06 1300.00 -169.06 305166.92
118 305166.92 1469.88 1300.00 -169.88 305336.80
119 305336.80 1470.69 1300.00 -170.69 305507.49
120 305507.49 1471.52 1300.00 -171.52 305679.01
121 305679.01 1472.34 1300.00 -172.34 305851.35
122 305851.35 1473.17 1300.00 -173.17 306024.52
123 306024.52 1474.01 1300.00 -174.01 306198.52
124 306198.52 1474.84 1300.00 -174.84 306373.37
125 306373.37 1475.69 1300.00 -175.69 306549.05
126 306549.05 1476.53 1300.00 -176.53 306725.59
127 306725.59 1477.38 1300.00 -177.38 306902.97
128 306902.97 1478.24 1300.00 -178.24 307081.21
129 307081.21 1479.10 1300.00 -179.10 307260.30
130 307260.30 1479.96 1300.00 -179.96 307440.26
131 307440.26 1480.82 1300.00 -180.82 307621.09
132 307621.09 1481.70 1300.00 -181.70 307802.78
133 307802.78 1482.57 1300.00 -182.57 307985.35
134 307985.35 1483.45 1300.00 -183.45 308168.80
135 308168.80 1484.33 1300.00 -184.33 308353.14
136 308353.14 1485.22 1300.00 -185.22 308538.36
137 308538.36 1486.11 1300.00 -186.11 308724.47
138 308724.47 1487.01 1300.00 -187.01 308911.48
139 308911.48 1487.91 1300.00 -187.91 309099.39
140 309099.39 1488.82 1300.00 -188.82 309288.21
141 309288.21 1489.73 1300.00 -189.73 309477.94
142 309477.94 1490.64 1300.00 -190.64 309668.58
143 309668.58 1491.56 1300.00 -191.56 309860.13
144 309860.13 1492.48 1300.00 -192.48 310052.61
145 310052.61 1493.41 1300.00 -193.41 310246.02
146 310246.02 1494.34 1300.00 -194.34 310440.36
147 310440.36 1495.28 1300.00 -195.28 310635.64
148 310635.64 1496.22 1300.00 -196.22 310831.85
149 310831.85 1497.16 1300.00 -197.16 311029.01
150 311029.01 1498.11 1300.00 -198.11 311227.12
151 311227.12 1499.06 1300.00 -199.06 311426.19
152 311426.19 1500.02 1300.00 -200.02 311626.21
153 311626.21 1500.99 1300.00 -200.99 311827.20
154 311827.20 1501.96 1300.00 -201.96 312029.15
155 312029.15 1502.93 1300.00 -202.93 312232.08
156 312232.08 1503.91 1300.00 -203.91 312435.99
157 312435.99 1504.89 1300.00 -204.89 312640.87
158 312640.87 1505.87 1300.00 -205.87 312846.75
159 312846.75 1506.87 1300.00 -206.87 313053.61
160 313053.61 1507.86 1300.00 -207.86 313261.48
161 313261.48 1508.86 1300.00 -208.86 313470.34
162 313470.34 1509.87 1300.00 -209.87 313680.21
163 313680.21 1510.88 1300.00 -210.88 313891.09
164 313891.09 1511.90 1300.00 -211.90 314102.99
165 314102.99 1512.92 1300.00 -212.92 314315.90
166 314315.90 1513.94 1300.00 -213.94 314529.85
167 314529.85 1514.97 1300.00 -214.97 314744.82
168 314744.82 1516.01 1300.00 -216.01 314960.83
169 314960.83 1517.05 1300.00 -217.05 315177.88
170 315177.88 1518.09 1300.00 -218.09 315395.97
171 315395.97 1519.14 1300.00 -219.14 315615.11
172 315615.11 1520.20 1300.00 -220.20 315835.31
173 315835.31 1521.26 1300.00 -221.26 316056.57
174 316056.57 1522.33 1300.00 -222.33 316278.90
175 316278.90 1523.40 1300.00 -223.40 316502.30
176 316502.30 1524.47 1300.00 -224.47 316726.77
177 316726.77 1525.55 1300.00 -225.55 316952.33
178 316952.33 1526.64 1300.00 -226.64 317178.97
179 317178.97 1527.73 1300.00 -227.73 317406.70
180 317406.70 1528.83 1300.00 -228.83 317635.53
181 317635.53 1529.93 1300.00 -229.93 317865.46
182 317865.46 1531.04 1300.00 -231.04 318096.50
183 318096.50 1532.15 1300.00 -232.15 318328.65
184 318328.65 1533.27 1300.00 -233.27 318561.92
185 318561.92 1534.39 1300.00 -234.39 318796.32
186 318796.32 1535.52 1300.00 -235.52 319031.84
187 319031.84 1536.66 1300.00 -236.66 319268.50
188 319268.50 1537.80 1300.00 -237.80 319506.29
189 319506.29 1538.94 1300.00 -238.94 319745.24
190 319745.24 1540.09 1300.00 -240.09 319985.33
191 319985.33 1541.25 1300.00 -241.25 320226.58
192 320226.58 1542.41 1300.00 -242.41 320468.99
193 320468.99 1543.58 1300.00 -243.58 320712.57
194 320712.57 1544.75 1300.00 -244.75 320957.32
195 320957.32 1545.93 1300.00 -245.93 321203.25
196 321203.25 1547.12 1300.00 -247.12 321450.37
197 321450.37 1548.31 1300.00 -248.31 321698.68
198 321698.68 1549.50 1300.00 -249.50 321948.18
199 321948.18 1550.70 1300.00 -250.70 322198.88
200 322198.88 1551.91 1300.00 -251.91 322450.79
201 322450.79 1553.13 1300.00 -253.13 322703.92
202 322703.92 1554.34 1300.00 -254.34 322958.26
203 322958.26 1555.57 1300.00 -255.57 323213.83
204 323213.83 1556.80 1300.00 -256.80 323470.63
205 323470.63 1558.04 1300.00 -258.04 323728.67
206 323728.67 1559.28 1300.00 -259.28 323987.95
207 323987.95 1560.53 1300.00 -260.53 324248.48
208 324248.48 1561.78 1300.00 -261.78 324510.26
209 324510.26 1563.04 1300.00 -263.04 324773.31
210 324773.31 1564.31 1300.00 -264.31 325037.62
211 325037.62 1565.58 1300.00 -265.58 325303.21
212 325303.21 1566.86 1300.00 -266.86 325570.07
213 325570.07 1568.15 1300.00 -268.15 325838.22
214 325838.22 1569.44 1300.00 -269.44 326107.66
215 326107.66 1570.74 1300.00 -270.74 326378.40
216 326378.40 1572.04 1300.00 -272.04 326650.44
217 326650.44 1573.35 1300.00 -273.35 326923.79
218 326923.79 1574.67 1300.00 -274.67 327198.46
219 327198.46 1575.99 1300.00 -275.99 327474.46
220 327474.46 1577.32 1300.00 -277.32 327751.78
221 327751.78 1578.66 1300.00 -278.66 328030.44
222 328030.44 1580.00 1300.00 -280.00 328310.44
223 328310.44 1581.35 1300.00 -281.35 328591.79
224 328591.79 1582.70 1300.00 -282.70 328874.49
225 328874.49 1584.07 1300.00 -284.07 329158.55
226 329158.55 1585.43 1300.00 -285.43 329443.99
227 329443.99 1586.81 1300.00 -286.81 329730.80
228 329730.80 1588.19 1300.00 -288.19 330018.99
229 330018.99 1589.58 1300.00 -289.58 330308.57
230 330308.57 1590.97 1300.00 -290.97 330599.54
231 330599.54 1592.37 1300.00 -292.37 330891.91
232 330891.91 1593.78 1300.00 -293.78 331185.70
233 331185.70 1595.20 1300.00 -295.20 331480.89
234 331480.89 1596.62 1300.00 -296.62 331777.51
235 331777.51 1598.05 1300.00 -298.05 332075.56
236 332075.56 1599.48 1300.00 -299.48 332375.05
237 332375.05 1600.93 1300.00 -300.93 332675.97
238 332675.97 1602.38 1300.00 -302.38 332978.35
239 332978.35 1603.83 1300.00 -303.83 333282.18
240 333282.18 1605.30 1300.00 -305.30 333587.48
241 333587.48 1606.77 1300.00 -306.77 333894.24
242 333894.24 1608.24 1300.00 -308.24 334202.49
243 334202.49 1609.73 1300.00 -309.73 334512.21
244 334512.21 1611.22 1300.00 -311.22 334823.43
245 334823.43 1612.72 1300.00 -312.72 335136.15
246 335136.15 1614.23 1300.00 -314.23 335450.38
247 335450.38 1615.74 1300.00 -315.74 335766.12
248 335766.12 1617.26 1300.00 -317.26 336083.38
249 336083.38 1618.79 1300.00 -318.79 336402.17
250 336402.17 1620.32 1300.00 -320.32 336722.49
251 336722.49 1621.87 1300.00 -321.87 337044.36
252 337044.36 1623.42 1300.00 -323.42 337367.77
253 337367.77 1624.97 1300.00 -324.97 337692.75
254 337692.75 1626.54 1300.00 -326.54 338019.29
255 338019.29 1628.11 1300.00 -328.11 338347.40
256 338347.40 1629.69 1300.00 -329.69 338677.09
257 338677.09 1631.28 1300.00 -331.28 339008.38
258 339008.38 1632.88 1300.00 -332.88 339341.25
259 339341.25 1634.48 1300.00 -334.48 339675.73
260 339675.73 1636.09 1300.00 -336.09 340011.82
261 340011.82 1637.71 1300.00 -337.71 340349.53
262 340349.53 1639.34 1300.00 -339.34 340688.87
263 340688.87 1640.97 1300.00 -340.97 341029.84
264 341029.84 1642.61 1300.00 -342.61 341372.45
265 341372.45 1644.26 1300.00 -344.26 341716.72
266 341716.72 1645.92 1300.00 -345.92 342062.64
267 342062.64 1647.59 1300.00 -347.59 342410.23
268 342410.23 1649.26 1300.00 -349.26 342759.49
269 342759.49 1650.94 1300.00 -350.94 343110.43
270 343110.43 1652.63 1300.00 -352.63 343463.07
271 343463.07 1654.33 1300.00 -354.33 343817.40
272 343817.40 1656.04 1300.00 -356.04 344173.44
273 344173.44 1657.75 1300.00 -357.75 344531.20
274 344531.20 1659.48 1300.00 -359.48 344890.67
275 344890.67 1661.21 1300.00 -361.21 345251.88
276 345251.88 1662.95 1300.00 -362.95 345614.83
277 345614.83 1664.70 1300.00 -364.70 345979.53
278 345979.53 1666.45 1300.00 -366.45 346345.99
279 346345.99 1668.22 1300.00 -368.22 346714.20
280 346714.20 1669.99 1300.00 -369.99 347084.20
281 347084.20 1671.77 1300.00 -371.77 347455.97
282 347455.97 1673.57 1300.00 -373.57 347829.54
283 347829.54 1675.36 1300.00 -375.36 348204.90
284 348204.90 1677.17 1300.00 -377.17 348582.08
285 348582.08 1678.99 1300.00 -378.99 348961.07
286 348961.07 1680.82 1300.00 -380.82 349341.88
287 349341.88 1682.65 1300.00 -382.65 349724.53
288 349724.53 1684.49 1300.00 -384.49 350109.02
289 350109.02 1686.34 1300.00 -386.34 350495.37
290 350495.37 1688.21 1300.00 -388.21 350883.57
291 350883.57 1690.08 1300.00 -390.08 351273.65
292 351273.65 1691.95 1300.00 -391.95 351665.60
293 351665.60 1693.84 1300.00 -393.84 352059.44
294 352059.44 1695.74 1300.00 -395.74 352455.18
295 352455.18 1697.64 1300.00 -397.64 352852.83
296 352852.83 1699.56 1300.00 -399.56 353252.39
297 353252.39 1701.48 1300.00 -401.48 353653.87
298 353653.87 1703.42 1300.00 -403.42 354057.29
299 354057.29 1705.36 1300.00 -405.36 354462.65
300 354462.65 1707.31 1300.00 -407.31 354869.97
301 354869.97 1709.28 1300.00 -409.28 355279.24
302 355279.24 1711.25 1300.00 -411.25 355690.49
303 355690.49 1713.23 1300.00 -413.23 356103.72
304 356103.72 1715.22 1300.00 -415.22 356518.94
305 356518.94 1717.22 1300.00 -417.22 356936.15
306 356936.15 1719.23 1300.00 -419.23 357355.38
307 357355.38 1721.25 1300.00 -421.25 357776.63
308 357776.63 1723.28 1300.00 -423.28 358199.91
309 358199.91 1725.32 1300.00 -425.32 358625.22
310 358625.22 1727.36 1300.00 -427.36 359052.59
311 359052.59 1729.42 1300.00 -429.42 359482.01
312 359482.01 1731.49 1300.00 -431.49 359913.50
313 359913.50 1733.57 1300.00 -433.57 360347.07
314 360347.07 1735.66 1300.00 -435.66 360782.72
315 360782.72 1737.76 1300.00 -437.76 361220.48
316 361220.48 1739.86 1300.00 -439.86 361660.34
317 361660.34 1741.98 1300.00 -441.98 362102.33
318 362102.33 1744.11 1300.00 -444.11 362546.44
319 362546.44 1746.25 1300.00 -446.25 362992.69
320 362992.69 1748.40 1300.00 -448.40 363441.09
321 363441.09 1750.56 1300.00 -450.56 363891.65
322 363891.65 1752.73 1300.00 -452.73 364344.38
323 364344.38 1754.91 1300.00 -454.91 364799.29
324 364799.29 1757.10 1300.00 -457.10 365256.39
325 365256.39 1759.30 1300.00 -459.30 365715.70
326 365715.70 1761.52 1300.00 -461.52 366177.21
327 366177.21 1763.74 1300.00 -463.74 366640.95
328 366640.95 1765.97 1300.00 -465.97 367106.92
329 367106.92 1768.22 1300.00 -468.22 367575.14
330 367575.14 1770.47 1300.00 -470.47 368045.61
331 368045.61 1772.74 1300.00 -472.74 368518.35
332 368518.35 1775.02 1300.00 -475.02 368993.37
333 368993.37 1777.30 1300.00 -477.30 369470.67
334 369470.67 1779.60 1300.00 -479.60 369950.27
335 369950.27 1781.91 1300.00 -481.91 370432.18
336 370432.18 1784.23 1300.00 -484.23 370916.42
337 370916.42 1786.57 1300.00 -486.57 371402.98
338 371402.98 1788.91 1300.00 -488.91 371891.89
339 371891.89 1791.26 1300.00 -491.26 372383.16
340 372383.16 1793.63 1300.00 -493.63 372876.79
341 372876.79 1796.01 1300.00 -496.01 373372.80
342 373372.80 1798.40 1300.00 -498.40 373871.19
343 373871.19 1800.80 1300.00 -500.80 374371.99
344 374371.99 1803.21 1300.00 -503.21 374875.20
345 374875.20 1805.63 1300.00 -505.63 375380.83
346 375380.83 1808.07 1300.00 -508.07 375888.90
347 375888.90 1810.52 1300.00 -510.52 376399.42
348 376399.42 1812.98 1300.00 -512.98 376912.40
349 376912.40 1815.45 1300.00 -515.45 377427.84
350 377427.84 1817.93 1300.00 -517.93 377945.77
351 377945.77 1820.42 1300.00 -520.42 378466.19
352 378466.19 1822.93 1300.00 -522.93 378989.12
353 378989.12 1825.45 1300.00 -525.45 379514.57
354 379514.57 1827.98 1300.00 -527.98 380042.55
355 380042.55 1830.52 1300.00 -530.52 380573.08
356 380573.08 1833.08 1300.00 -533.08 381106.15
357 381106.15 1835.65 1300.00 -535.65 381641.80
358 381641.80 1838.23 1300.00 -538.23 382180.03
359 382180.03 1840.82 1300.00 -540.82 382720.84
360 382720.84 1843.42 1300.00 -543.42 383264.27

Formula used: r is monthly interest rate computed above.

Hence, balloon payment will be of $ 383264.27


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