Question

HSBC decided to give Frank Broke a $800,000 mortgage loan at a rate of 3% for 30 years: (a) What will be Frank’s monthly payments if he is expected to pay back the loan at the end of each month? (5 Points) (b) How much interest and principal will Frank pay from the start of the third year (January) to the end of the fourth year (December)? (5 Points) [You MUST use a financial calculator, an APP, or Excel to solve the problem. Although you may use a template to check your answers, you must write out your own algorithm if you decide to use an Excel spreadsheet]. Collect data on the CPI and real GDP for 10 years, using a 2% bench mark for inflation and GDP growth evaluate the Taylor rule. Plot the graph for the Federal Funds Rate and your estimated rate. (You can annualize quarterly data. Evaluate your findings in the light of the Taylor rule.

Answer 1

A.

Monthly rate R = 3%/12 = ..25%

Time = 360 months

Loan amount = $800000

So,

Monthly payment = 800000/((1-1/1.0025^360)/.0025)

Monthly payment = $3372.83 or $3373

B.

Principal amount left for the payment after 2 years (24 months) = 800000*(1+.25%)^24 - 3373*((1+.25%)^24 -1)/.0025

Principal amount left for the payment after 2 years (24 months) = $766083

Principal amount left for the payment after 4 years (48 months) = 800000*(1+.25%)^48 - 3373*((1+.25%)^48 -1)/.0025

Principal amount left for the payment after 2 years (24 months) = $730071.42

So,

Principal amount paid in 2 years ( from 3rd year to end of 4th year) = 766083-730071.42

principal amount paid in 2 years ( from 3rd year to end of 4th year) = $36011.58

Interest paid in 2 years ( from 3rd year to end of 4th year) = 24*3373 - 36011.5 = $44940.42

Working note:

Month EMI Interest Principal Loan left

25	3373	1915.21	1457.79	764625.24
26	3373	1911.56	1461.44	763163.80
27	3373	1907.91	1465.09	761698.71
28	3373	1904.25	1468.75	760229.96
29	3373	1900.57	1472.43	758757.53
30	3373	1896.89	1476.11	757281.43
31	3373	1893.20	1479.80	755801.63
32	3373	1889.50	1483.50	754318.13
33	3373	1885.80	1487.20	752830.93
34	3373	1882.08	1490.92	751340.01
35	3373	1878.35	1494.65	749845.36
36	3373	1874.61	1498.39	748346.97
37	3373	1870.87	1502.13	746844.84
38	3373	1867.11	1505.89	745338.95
39	3373	1863.35	1509.65	743829.30
40	3373	1859.57	1513.43	742315.87
41	3373	1855.79	1517.21	740798.66
42	3373	1852.00	1521.00	739277.66
43	3373	1848.19	1524.81	737752.85
44	3373	1844.38	1528.62	736224.23
45	3373	1840.56	1532.44	734691.79
46	3373	1836.73	1536.27	733155.52
47	3373	1832.89	1540.11	731615.41
48	3373	1829.04	1543.96	730071.45

Total interest=$44940.42 Principal paid = $36011.58

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