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 Help from Math Experts, please.
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Posted on 01-09-15 3:42 PM     Reply [Subscribe]
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Hi,
I need to calculate fixed yearly interest rate. Here's the problem:
Amount: $84289.80
Number of monthly payments: 231
Monthly payment: $528.67

Thanks.
 
Posted on 01-09-15 5:05 PM     [Snapshot: 58]     Reply [Subscribe]
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4.110036%
 
Posted on 01-09-15 5:51 PM     [Snapshot: 103]     Reply [Subscribe]
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can you post how you figured it out?
 
Posted on 01-10-15 6:15 AM     [Snapshot: 277]     Reply [Subscribe]
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Yes can you tell me how you came with this number? I got 3.08% interest rate.
Is there a specific forumla?
 
Posted on 01-10-15 8:04 AM     [Snapshot: 319]     Reply [Subscribe]
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i got 2.025%
lol
 
Posted on 01-10-15 11:15 AM     [Snapshot: 399]     Reply [Subscribe]
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Answer is 4.11
 
Posted on 01-10-15 12:18 PM     [Snapshot: 447]     Reply [Subscribe]
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Yikes! This problem isn't as simple as I thought. I already spent a couple of hours still couldn't get through. However, I found an example in following website, and I assume it might be helpful to solve it. If u r able to solve this problem please post the steps here. And I think 4.11% is the right answer because when u plug into a right online calculator you can get that answer.
http://mathforum.org/dr.math/faq/faq.interest.html
 
Posted on 01-10-15 7:23 PM     [Snapshot: 541]     Reply [Subscribe]
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I know the steps but its too long to post here. Sorry. It just took me 12 minutes to solve this problem.
 
Posted on 01-10-15 11:42 PM     [Snapshot: 638]     Reply [Subscribe]
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The answer seems to be 4.11 using HP 12C calculator.
I think the math behind this calculation is
PV/PMT = ((1-(1+i)^n)/i
where PV=84289.80
PMT= 528.67
n = 231
find i
 
Posted on 01-11-15 12:37 AM     [Snapshot: 655]     Reply [Subscribe]
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4.11 seems right,
 M = P * ( J / (1 - (1 + J)-N))
  • M = payment amount
  • P = principal, meaning the amount of money borrowed
  • J = effective interest rate.
  • N = total number of payments
here is how your payment would get allocated.
Month Balance Principal Interest Payment
1 $ 84,289.80 $ 239.98 $ 288.69 $ 528.67
2 $ 84,049.82 $ 240.80 $ 287.87 $ 528.67
3 $ 83,809.03 $ 241.62 $ 287.05 $ 528.67
4 $ 83,567.40 $ 242.45 $ 286.22 $ 528.67
5 $ 83,324.95 $ 243.28 $ 285.39 $ 528.67
6 $ 83,081.67 $ 244.11 $ 284.55 $ 528.67
7 $ 82,837.56 $ 244.95 $ 283.72 $ 528.67
8 $ 82,592.61 $ 245.79 $ 282.88 $ 528.67
9 $ 82,346.82 $ 246.63 $ 282.04 $ 528.67
10 $ 82,100.19 $ 247.48 $ 281.19 $ 528.67
11 $ 81,852.72 $ 248.32 $ 280.35 $ 528.67
12 $ 81,604.39 $ 249.17 $ 279.50 $ 528.67
13 $ 81,355.22 $ 250.03 $ 278.64 $ 528.67
14 $ 81,105.19 $ 250.88 $ 277.79 $ 528.67
15 $ 80,854.31 $ 251.74 $ 276.93 $ 528.67
16 $ 80,602.57 $ 252.60 $ 276.06 $ 528.67
17 $ 80,349.96 $ 253.47 $ 275.20 $ 528.67
18 $ 80,096.49 $ 254.34 $ 274.33 $ 528.67
19 $ 79,842.16 $ 255.21 $ 273.46 $ 528.67
20 $ 79,586.95 $ 256.08 $ 272.59 $ 528.67
21 $ 79,330.86 $ 256.96 $ 271.71 $ 528.67
22 $ 79,073.90 $ 257.84 $ 270.83 $ 528.67
23 $ 78,816.06 $ 258.72 $ 269.95 $ 528.67
24 $ 78,557.34 $ 259.61 $ 269.06 $ 528.67
25 $ 78,297.73 $ 260.50 $ 268.17 $ 528.67
26 $ 78,037.23 $ 261.39 $ 267.28 $ 528.67
27 $ 77,775.84 $ 262.29 $ 266.38 $ 528.67
28 $ 77,513.55 $ 263.18 $ 265.48 $ 528.67
29 $ 77,250.37 $ 264.09 $ 264.58 $ 528.67
30 $ 76,986.28 $ 264.99 $ 263.68 $ 528.67
31 $ 76,721.29 $ 265.90 $ 262.77 $ 528.67
32 $ 76,455.40 $ 266.81 $ 261.86 $ 528.67
33 $ 76,188.59 $ 267.72 $ 260.95 $ 528.67
34 $ 75,920.86 $ 268.64 $ 260.03 $ 528.67
35 $ 75,652.22 $ 269.56 $ 259.11 $ 528.67
36 $ 75,382.67 $ 270.48 $ 258.19 $ 528.67
37 $ 75,112.18 $ 271.41 $ 257.26 $ 528.67
38 $ 74,840.77 $ 272.34 $ 256.33 $ 528.67
39 $ 74,568.43 $ 273.27 $ 255.40 $ 528.67
40 $ 74,295.16 $ 274.21 $ 254.46 $ 528.67
41 $ 74,020.96 $ 275.15 $ 253.52 $ 528.67
42 $ 73,745.81 $ 276.09 $ 252.58 $ 528.67
43 $ 73,469.72 $ 277.03 $ 251.63 $ 528.67
44 $ 73,192.69 $ 277.98 $ 250.68 $ 528.67
45 $ 72,914.70 $ 278.94 $ 249.73 $ 528.67
46 $ 72,635.77 $ 279.89 $ 248.78 $ 528.67
47 $ 72,355.88 $ 280.85 $ 247.82 $ 528.67
48 $ 72,075.03 $ 281.81 $ 246.86 $ 528.67
49 $ 71,793.21 $ 282.78 $ 245.89 $ 528.67
50 $ 71,510.44 $ 283.75 $ 244.92 $ 528.67
51 $ 71,226.69 $ 284.72 $ 243.95 $ 528.67
52 $ 70,941.98 $ 285.69 $ 242.98 $ 528.67
53 $ 70,656.28 $ 286.67 $ 242.00 $ 528.67
54 $ 70,369.61 $ 287.65 $ 241.02 $ 528.67
55 $ 70,081.96 $ 288.64 $ 240.03 $ 528.67
56 $ 69,793.32 $ 289.63 $ 239.04 $ 528.67
57 $ 69,503.70 $ 290.62 $ 238.05 $ 528.67
58 $ 69,213.08 $ 291.61 $ 237.05 $ 528.67
59 $ 68,921.47 $ 292.61 $ 236.06 $ 528.67
60 $ 68,628.85 $ 293.61 $ 235.05 $ 528.67
61 $ 68,335.24 $ 294.62 $ 234.05 $ 528.67
62 $ 68,040.62 $ 295.63 $ 233.04 $ 528.67
63 $ 67,744.99 $ 296.64 $ 232.03 $ 528.67
64 $ 67,448.35 $ 297.66 $ 231.01 $ 528.67
65 $ 67,150.69 $ 298.68 $ 229.99 $ 528.67
66 $ 66,852.01 $ 299.70 $ 228.97 $ 528.67
67 $ 66,552.31 $ 300.73 $ 227.94 $ 528.67
68 $ 66,251.58 $ 301.76 $ 226.91 $ 528.67
69 $ 65,949.83 $ 302.79 $ 225.88 $ 528.67
70 $ 65,647.04 $ 303.83 $ 224.84 $ 528.67
71 $ 65,343.21 $ 304.87 $ 223.80 $ 528.67
72 $ 65,038.34 $ 305.91 $ 222.76 $ 528.67
73 $ 64,732.43 $ 306.96 $ 221.71 $ 528.67
74 $ 64,425.47 $ 308.01 $ 220.66 $ 528.67
75 $ 64,117.46 $ 309.07 $ 219.60 $ 528.67
76 $ 63,808.39 $ 310.12 $ 218.54 $ 528.67
77 $ 63,498.27 $ 311.19 $ 217.48 $ 528.67
78 $ 63,187.08 $ 312.25 $ 216.42 $ 528.67
79 $ 62,874.83 $ 313.32 $ 215.35 $ 528.67
80 $ 62,561.51 $ 314.40 $ 214.27 $ 528.67
81 $ 62,247.11 $ 315.47 $ 213.20 $ 528.67
82 $ 61,931.64 $ 316.55 $ 212.12 $ 528.67
83 $ 61,615.09 $ 317.64 $ 211.03 $ 528.67
84 $ 61,297.45 $ 318.72 $ 209.94 $ 528.67
85 $ 60,978.73 $ 319.82 $ 208.85 $ 528.67
86 $ 60,658.91 $ 320.91 $ 207.76 $ 528.67
87 $ 60,338.00 $ 322.01 $ 206.66 $ 528.67
88 $ 60,015.99 $ 323.11 $ 205.55 $ 528.67
89 $ 59,692.87 $ 324.22 $ 204.45 $ 528.67
90 $ 59,368.65 $ 325.33 $ 203.34 $ 528.67
91 $ 59,043.32 $ 326.45 $ 202.22 $ 528.67
92 $ 58,716.88 $ 327.56 $ 201.11 $ 528.67
93 $ 58,389.32 $ 328.68 $ 199.98 $ 528.67
94 $ 58,060.63 $ 329.81 $ 198.86 $ 528.67
95 $ 57,730.82 $ 330.94 $ 197.73 $ 528.67
96 $ 57,399.88 $ 332.07 $ 196.59 $ 528.67
97 $ 57,067.81 $ 333.21 $ 195.46 $ 528.67
98 $ 56,734.59 $ 334.35 $ 194.32 $ 528.67
99 $ 56,400.24 $ 335.50 $ 193.17 $ 528.67
100 $ 56,064.74 $ 336.65 $ 192.02 $ 528.67
101 $ 55,728.10 $ 337.80 $ 190.87 $ 528.67
102 $ 55,390.30 $ 338.96 $ 189.71 $ 528.67
103 $ 55,051.34 $ 340.12 $ 188.55 $ 528.67
104 $ 54,711.22 $ 341.28 $ 187.39 $ 528.67
105 $ 54,369.94 $ 342.45 $ 186.22 $ 528.67
106 $ 54,027.49 $ 343.62 $ 185.04 $ 528.67
107 $ 53,683.87 $ 344.80 $ 183.87 $ 528.67
108 $ 53,339.06 $ 345.98 $ 182.69 $ 528.67
109 $ 52,993.08 $ 347.17 $ 181.50 $ 528.67
110 $ 52,645.92 $ 348.36 $ 180.31 $ 528.67
111 $ 52,297.56 $ 349.55 $ 179.12 $ 528.67
112 $ 51,948.01 $ 350.75 $ 177.92 $ 528.67
113 $ 51,597.26 $ 351.95 $ 176.72 $ 528.67
114 $ 51,245.32 $ 353.15 $ 175.52 $ 528.67
115 $ 50,892.16 $ 354.36 $ 174.31 $ 528.67
116 $ 50,537.80 $ 355.58 $ 173.09 $ 528.67
117 $ 50,182.22 $ 356.79 $ 171.87 $ 528.67
118 $ 49,825.43 $ 358.02 $ 170.65 $ 528.67
119 $ 49,467.41 $ 359.24 $ 169.43 $ 528.67
120 $ 49,108.17 $ 360.47 $ 168.20 $ 528.67
121 $ 48,747.70 $ 361.71 $ 166.96 $ 528.67
122 $ 48,385.99 $ 362.95 $ 165.72 $ 528.67
123 $ 48,023.04 $ 364.19 $ 164.48 $ 528.67
124 $ 47,658.85 $ 365.44 $ 163.23 $ 528.67
125 $ 47,293.42 $ 366.69 $ 161.98 $ 528.67
126 $ 46,926.73 $ 367.94 $ 160.72 $ 528.67
127 $ 46,558.78 $ 369.20 $ 159.46 $ 528.67
128 $ 46,189.58 $ 370.47 $ 158.20 $ 528.67
129 $ 45,819.11 $ 371.74 $ 156.93 $ 528.67
130 $ 45,447.37 $ 373.01 $ 155.66 $ 528.67
131 $ 45,074.36 $ 374.29 $ 154.38 $ 528.67
132 $ 44,700.07 $ 375.57 $ 153.10 $ 528.67
133 $ 44,324.50 $ 376.86 $ 151.81 $ 528.67
134 $ 43,947.65 $ 378.15 $ 150.52 $ 528.67
135 $ 43,569.50 $ 379.44 $ 149.23 $ 528.67
136 $ 43,190.06 $ 380.74 $ 147.93 $ 528.67
137 $ 42,809.31 $ 382.05 $ 146.62 $ 528.67
138 $ 42,427.27 $ 383.35 $ 145.31 $ 528.67
139 $ 42,043.91 $ 384.67 $ 144.00 $ 528.67
140 $ 41,659.24 $ 385.99 $ 142.68 $ 528.67
141 $ 41,273.26 $ 387.31 $ 141.36 $ 528.67
142 $ 40,885.95 $ 388.63 $ 140.03 $ 528.67
143 $ 40,497.32 $ 389.97 $ 138.70 $ 528.67
144 $ 40,107.35 $ 391.30 $ 137.37 $ 528.67
145 $ 39,716.05 $ 392.64 $ 136.03 $ 528.67
146 $ 39,323.41 $ 393.99 $ 134.68 $ 528.67
147 $ 38,929.42 $ 395.34 $ 133.33 $ 528.67
148 $ 38,534.09 $ 396.69 $ 131.98 $ 528.67
149 $ 38,137.40 $ 398.05 $ 130.62 $ 528.67
150 $ 37,739.35 $ 399.41 $ 129.26 $ 528.67
151 $ 37,339.94 $ 400.78 $ 127.89 $ 528.67
152 $ 36,939.16 $ 402.15 $ 126.52 $ 528.67
153 $ 36,537.01 $ 403.53 $ 125.14 $ 528.67
154 $ 36,133.48 $ 404.91 $ 123.76 $ 528.67
155 $ 35,728.57 $ 406.30 $ 122.37 $ 528.67
156 $ 35,322.27 $ 407.69 $ 120.98 $ 528.67
157 $ 34,914.58 $ 409.09 $ 119.58 $ 528.67
158 $ 34,505.50 $ 410.49 $ 118.18 $ 528.67
159 $ 34,095.01 $ 411.89 $ 116.78 $ 528.67
160 $ 33,683.12 $ 413.30 $ 115.36 $ 528.67
161 $ 33,269.81 $ 414.72 $ 113.95 $ 528.67
162 $ 32,855.09 $ 416.14 $ 112.53 $ 528.67
163 $ 32,438.95 $ 417.56 $ 111.10 $ 528.67
164 $ 32,021.39 $ 419.00 $ 109.67 $ 528.67
165 $ 31,602.39 $ 420.43 $ 108.24 $ 528.67
166 $ 31,181.96 $ 421.87 $ 106.80 $ 528.67
167 $ 30,760.09 $ 423.32 $ 105.35 $ 528.67
168 $ 30,336.78 $ 424.76 $ 103.90 $ 528.67
169 $ 29,912.01 $ 426.22 $ 102.45 $ 528.67
170 $ 29,485.79 $ 427.68 $ 100.99 $ 528.67
171 $ 29,058.11 $ 429.14 $ 99.52 $ 528.67
172 $ 28,628.97 $ 430.61 $ 98.05 $ 528.67
173 $ 28,198.36 $ 432.09 $ 96.58 $ 528.67
174 $ 27,766.27 $ 433.57 $ 95.10 $ 528.67
175 $ 27,332.70 $ 435.05 $ 93.61 $ 528.67
176 $ 26,897.64 $ 436.54 $ 92.12 $ 528.67
177 $ 26,461.10 $ 438.04 $ 90.63 $ 528.67
178 $ 26,023.06 $ 439.54 $ 89.13 $ 528.67
179 $ 25,583.52 $ 441.04 $ 87.62 $ 528.67
180 $ 25,142.48 $ 442.56 $ 86.11 $ 528.67
181 $ 24,699.92 $ 444.07 $ 84.60 $ 528.67
182 $ 24,255.85 $ 445.59 $ 83.08 $ 528.67
183 $ 23,810.26 $ 447.12 $ 81.55 $ 528.67
184 $ 23,363.14 $ 448.65 $ 80.02 $ 528.67
185 $ 22,914.49 $ 450.19 $ 78.48 $ 528.67
186 $ 22,464.30 $ 451.73 $ 76.94 $ 528.67
187 $ 22,012.57 $ 453.28 $ 75.39 $ 528.67
188 $ 21,559.30 $ 454.83 $ 73.84 $ 528.67
189 $ 21,104.47 $ 456.39 $ 72.28 $ 528.67
190 $ 20,648.09 $ 457.95 $ 70.72 $ 528.67
191 $ 20,190.14 $ 459.52 $ 69.15 $ 528.67
192 $ 19,730.62 $ 461.09 $ 67.58 $ 528.67
193 $ 19,269.53 $ 462.67 $ 66.00 $ 528.67
194 $ 18,806.86 $ 464.25 $ 64.41 $ 528.67
195 $ 18,342.60 $ 465.84 $ 62.82 $ 528.67
196 $ 17,876.76 $ 467.44 $ 61.23 $ 528.67
197 $ 17,409.32 $ 469.04 $ 59.63 $ 528.67
198 $ 16,940.28 $ 470.65 $ 58.02 $ 528.67
199 $ 16,469.63 $ 472.26 $ 56.41 $ 528.67
200 $ 15,997.37 $ 473.88 $ 54.79 $ 528.67
201 $ 15,523.49 $ 475.50 $ 53.17 $ 528.67
202 $ 15,047.99 $ 477.13 $ 51.54 $ 528.67
203 $ 14,570.86 $ 478.76 $ 49.91 $ 528.67
204 $ 14,092.10 $ 480.40 $ 48.27 $ 528.67
205 $ 13,611.70 $ 482.05 $ 46.62 $ 528.67
206 $ 13,129.65 $ 483.70 $ 44.97 $ 528.67
207 $ 12,645.95 $ 485.36 $ 43.31 $ 528.67
208 $ 12,160.59 $ 487.02 $ 41.65 $ 528.67
209 $ 11,673.57 $ 488.69 $ 39.98 $ 528.67
210 $ 11,184.89 $ 490.36 $ 38.31 $ 528.67
211 $ 10,694.53 $ 492.04 $ 36.63 $ 528.67
212 $ 10,202.49 $ 493.72 $ 34.94 $ 528.67
213 $ 9,708.76 $ 495.42 $ 33.25 $ 528.67
214 $ 9,213.35 $ 497.11 $ 31.56 $ 528.67
215 $ 8,716.23 $ 498.82 $ 29.85 $ 528.67
216 $ 8,217.42 $ 500.52 $ 28.14 $ 528.67
217 $ 7,716.90 $ 502.24 $ 26.43 $ 528.67
218 $ 7,214.66 $ 503.96 $ 24.71 $ 528.67
219 $ 6,710.70 $ 505.68 $ 22.98 $ 528.67
220 $ 6,205.02 $ 507.42 $ 21.25 $ 528.67
221 $ 5,697.60 $ 509.15 $ 19.51 $ 528.67
222 $ 5,188.45 $ 510.90 $ 17.77 $ 528.67
223 $ 4,677.55 $ 512.65 $ 16.02 $ 528.67
224 $ 4,164.90 $ 514.40 $ 14.26 $ 528.67
225 $ 3,650.50 $ 516.17 $ 12.50 $ 528.67
226 $ 3,134.33 $ 517.93 $ 10.74 $ 528.67
227 $ 2,616.40 $ 519.71 $ 8.96 $ 528.67
228 $ 2,096.69 $ 521.49 $ 7.18 $ 528.67
229 $ 1,575.20 $ 523.27 $ 5.40 $ 528.67
230 $ 1,051.93 $ 525.07 $ 3.60 $ 528.67
231 $ 526.86 $ 526.86 $ 1.80 $ 528.67
Last edited: 11-Jan-15 01:08 AM
 

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