In: Finance
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%
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