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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