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At what nominal annual rate of interest will a $196,000 variable-rate mortgage be amortized by monthly...

At what nominal annual rate of interest will a $196,000 variable-rate mortgage be amortized by monthly payments of $1,666.87 over 20 years? Assume interest is compounded semi-annually.

Select one:

a. 8.54%

b. 8.37%

c. 5.54%

d. 7.54%

e. 6.54%

Solutions

Expert Solution

Monthly rate(M)= yearly rate/12= 0.69% Monthly payment= 1666.87
Month Beginning balance (A) Monthly payment Interest = M*A Principal paid Ending balance
1 196000.00 1666.87 1343.28 323.59 195676.41
2 195676.41 1666.87 1341.06 325.81 195350.60
3 195350.60 1666.87 1338.83 328.04 195022.56
4 195022.56 1666.87 1336.58 330.29 194692.26
5 194692.26 1666.87 1334.32 332.55 194359.71
6 194359.71 1666.87 1332.04 334.83 194024.88
7 194024.88 1666.87 1329.74 337.13 193687.75
8 193687.75 1666.87 1327.43 339.44 193348.31
9 193348.31 1666.87 1325.10 341.77 193006.54
10 193006.54 1666.87 1322.76 344.11 192662.44
11 192662.44 1666.87 1320.40 346.47 192315.97
12 192315.97 1666.87 1318.03 348.84 191967.13
13 191967.13 1666.87 1315.64 351.23 191615.90
14 191615.90 1666.87 1313.23 353.64 191262.26
15 191262.26 1666.87 1310.81 356.06 190906.20
16 190906.20 1666.87 1308.37 358.50 190547.70
17 190547.70 1666.87 1305.91 360.96 190186.74
18 190186.74 1666.87 1303.44 363.43 189823.30
19 189823.30 1666.87 1300.95 365.92 189457.38
20 189457.38 1666.87 1298.44 368.43 189088.95
21 189088.95 1666.87 1295.91 370.96 188717.99
22 188717.99 1666.87 1293.37 373.50 188344.49
23 188344.49 1666.87 1290.81 376.06 187968.44
24 187968.44 1666.87 1288.23 378.64 187589.80
25 187589.80 1666.87 1285.64 381.23 187208.57
26 187208.57 1666.87 1283.03 383.84 186824.72
27 186824.72 1666.87 1280.40 386.47 186438.25
28 186438.25 1666.87 1277.75 389.12 186049.13
29 186049.13 1666.87 1275.08 391.79 185657.34
30 185657.34 1666.87 1272.39 394.48 185262.86
31 185262.86 1666.87 1269.69 397.18 184865.68
32 184865.68 1666.87 1266.97 399.90 184465.78
33 184465.78 1666.87 1264.23 402.64 184063.14
34 184063.14 1666.87 1261.47 405.40 183657.74
35 183657.74 1666.87 1258.69 408.18 183249.56

.

.

.

.

219 33932.82 1666.87 232.56 1434.31 32498.51
220 32498.51 1666.87 222.73 1444.14 31054.37
221 31054.37 1666.87 212.83 1454.04 29600.33
222 29600.33 1666.87 202.86 1464.01 28136.32
223 28136.32 1666.87 192.83 1474.04 26662.28
224 26662.28 1666.87 182.73 1484.14 25178.14
225 25178.14 1666.87 172.56 1494.31 23683.83
226 23683.83 1666.87 162.32 1504.55 22179.28
227 22179.28 1666.87 152.00 1514.87 20664.41
228 20664.41 1666.87 141.62 1525.25 19139.16
229 19139.16 1666.87 131.17 1535.70 17603.46
230 17603.46 1666.87 120.64 1546.23 16057.24
231 16057.24 1666.87 110.05 1556.82 14500.42
232 14500.42 1666.87 99.38 1567.49 12932.92
233 12932.92 1666.87 88.64 1578.23 11354.69
234 11354.69 1666.87 77.82 1589.05 9765.64
235 9765.64 1666.87 66.93 1599.94 8165.70
236 8165.70 1666.87 55.96 1610.91 6554.79
237 6554.79 1666.87 44.92 1621.95 4932.84
238 4932.84 1666.87 33.81 1633.06 3299.78
239 3299.78 1666.87 22.61 1644.26 1655.52
240 1655.52 1666.87 11.35 1655.52 0.00
Annual rate %=8.22
Where
Interest paid = Beginning balance * Monthly interest rate
Principal = Monthly payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Month ending balance
EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100
Effective Annual Rate = ((1+8.22/2*100)^2-1)*100
Effective Annual Rate% = 8.39

b is correct

jeff jeffy answered 1 year ago
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