Question

James King bought a house three years ago that cost $750,000. James put up 20% deposit and borrowed the rest from FC Bank at a rate of 7.2% per annum, compounded monthly, for 10 years.

Three months ago, FC Bank notified James that after the last monthly payment for the third year, the interest rate on his loan will increase to 9.6% per annum, compounded monthly, in line with market rates. Also, from the fourth year of his loan James can either increase the monthly repayment (so as to pay off the loan by the originally agreed date), or he can keep paying the same original monthly repayment and extend the term of the loan.

1. Calculate the new monthly repayment if James pays off the loan by the originally agreeddate.
2. Calculate the extra period added to the term of the loan, if James keeps on paying the original monthly repayment.

Answer 1

a). Total cost = 750,000

Down-payment = 20%

Mortgage amount = 750,000*(1-20%) = 600,000

Annual interest rate = 7.2% so monthly rate = 7.2%/12 = 0.60%

Duration = 10 years or 10*12 = 120 payments.

Monthly payment: I/Y = 0.60%; N = 120; PV = 600,000, solve for PMT.

PMT = 7,028.51

Loan amortization schedule for 3 years:

	(a)	(b)	(c = 0.6%*a)	(d = a-c)	(e = b-d)
Number of payments	Monthly payment	Beg. Principal	Interest	Principal	End. Principal
1	7,028.51	600,000.00	3,600.00	3,428.51	596,571.49
2	7,028.51	596,571.49	3,579.43	3,449.08	593,122.40
3	7,028.51	593,122.40	3,558.73	3,469.78	589,652.63
4	7,028.51	589,652.63	3,537.92	3,490.60	586,162.03
5	7,028.51	586,162.03	3,516.97	3,511.54	582,650.49
6	7,028.51	582,650.49	3,495.90	3,532.61	579,117.88
7	7,028.51	579,117.88	3,474.71	3,553.81	575,564.07
8	7,028.51	575,564.07	3,453.38	3,575.13	571,988.95
9	7,028.51	571,988.95	3,431.93	3,596.58	568,392.37
10	7,028.51	568,392.37	3,410.35	3,618.16	564,774.21
11	7,028.51	564,774.21	3,388.65	3,639.87	561,134.34
12	7,028.51	561,134.34	3,366.81	3,661.71	557,472.64
13	7,028.51	557,472.64	3,344.84	3,683.68	553,788.96
14	7,028.51	553,788.96	3,322.73	3,705.78	550,083.18
15	7,028.51	550,083.18	3,300.50	3,728.01	546,355.17
16	7,028.51	546,355.17	3,278.13	3,750.38	542,604.79
17	7,028.51	542,604.79	3,255.63	3,772.88	538,831.90
18	7,028.51	538,831.90	3,232.99	3,795.52	535,036.38
19	7,028.51	535,036.38	3,210.22	3,818.29	531,218.09
20	7,028.51	531,218.09	3,187.31	3,841.20	527,376.88
21	7,028.51	527,376.88	3,164.26	3,864.25	523,512.63
22	7,028.51	523,512.63	3,141.08	3,887.44	519,625.19
23	7,028.51	519,625.19	3,117.75	3,910.76	515,714.43
24	7,028.51	515,714.43	3,094.29	3,934.23	511,780.21
25	7,028.51	511,780.21	3,070.68	3,957.83	507,822.38
26	7,028.51	507,822.38	3,046.93	3,981.58	503,840.80
27	7,028.51	503,840.80	3,023.04	4,005.47	499,835.33
28	7,028.51	499,835.33	2,999.01	4,029.50	495,805.83
29	7,028.51	495,805.83	2,974.83	4,053.68	491,752.15
30	7,028.51	91,752.15	2,950.51	4,078.00	487,674.15
31	7,028.51	487,674.15	2,926.04	4,102.47	483,571.69
32	7,028.51	483,571.69	2,901.43	4,127.08	479,444.60
33	7,028.51	479,444.60	2,876.67	4,151.84	475,292.76
34	7,028.51	475,292.76	2,851.76	4,176.76	471,116.00
35	7,028.51	471,116.00	2,826.70	4,201.82	466,914.19
36	7,028.51	466,914.19	2,801.49	4,227.03	462,687.16

Principal remaining after 3 years = 462,687.16

New interest rate p.a. = 9.6% so monthly rate = 9.6%/12 = 0.8%

Loan duration remaining = 10-3 = 7 years or 7*12 = 84 payments

Solve for PMT: I/Y = 0.80%; N = 84; PV = 462,687.16

PMT = 7,585.87 (new monthly payment)

b). If monthly payment remains 7,028.51 then number of payments can be calculated using present value of annuity formula:

PV = PMT *(1 - (1+r)^-n)/r

PV*r/PMT = 1 - (1+r)^-n

462,687.16*0.80%/7,028.51 = 1 - (1.008)^-n

(1.008)^-n = 1 - 0.5266

1.008^-n = 0.4734

Taking log on both sides, n = 93.86

Approx.93.86 or 94 payments will be needed.

This is 94-84 = 10 payments more than the original term of the loan.