Question

Arthur and Rebecca have been married for one year, and are planning to buy a house in Canberra for $900,000. They will borrow $600,000 from a bank. The interest rate on the loan is 4.00% per annum, compounding quarterly. The loan is for 30 years, and they have to make quarterly repayments to the bank, the first payment being exactly three months (i.e. one quarter) from today. What is the amount of the quarterly repayment?

Select one:

a. $8,458.77

b. $10,152.36

c. $12,912.39

d. $8,608.26

Answer 1

Computation of the Quartely installment amount

Loan Amount = $ 600000

Interest rate = 4% per annum Compounding Quarterly

No.of Years = 30

No.of Quarterly Repayments = 4*30=120

Interest rate per Quarter = 4% /4 = 1% per Quarter.

S.No	Disc @ 1%	Disc @ 1%
1	1/1.01	0.99009901
2	(1/1.01)^2	0.980296049
3	(1/1.01)^3	0.970590148
4	(1/1.01)^4	0.960980344
5	(1/1.01)^5	0.951465688
6	(1/1.01)^6	0.942045235
7	(1/1.01)^7	0.932718055
8	(1/1.01)^8	0.923483222
9	(1/1.01)^9	0.914339824
10	(1/1.01)^10	0.905286955
11	(1/1.01)^11	0.896323718
12	(1/1.01)^12	0.887449225
13	(1/1.01)^13	0.878662599
14	(1/1.01)^14	0.86996297
15	(1/1.01)^15	0.861349475
16	(1/1.01)^16	0.852821262
17	(1/1.01)^17	0.844377487
18	(1/1.01)^18	0.836017314
19	(1/1.01)^19	0.827739915
20	(1/1.01)^20	0.81954447
21	(1/1.01)^21	0.811430169
22	(1/1.01)^22	0.803396207
23	(1/1.01)^23	0.795441789
24	(1/1.01)^24	0.787566127
25	(1/1.01)^25	0.779768443
26	(1/1.01)^26	0.772047963
27	(1/1.01)^27	0.764403924
28	(1/1.01)^28	0.756835568
29	(1/1.01)^29	0.749342147
30	(1/1.01)^30	0.741922918
31	(1/1.01)^31	0.734577146
32	(1/1.01)^32	0.727304105
33	(1/1.01)^33	0.720103075
34	(1/1.01)^34	0.712973341
35	(1/1.01)^35	0.705914199
36	(1/1.01)^36	0.69892495
37	(1/1.01)^37	0.692004901
38	(1/1.01)^38	0.685153367
39	(1/1.01)^39	0.67836967
40	(1/1.01)^40	0.671653139
41	(1/1.01)^41	0.665003108
42	(1/1.01)^42	0.658418919
43	(1/1.01)^43	0.651899919
44	(1/1.01)^44	0.645445465
45	(1/1.01)^45	0.639054916
46	(1/1.01)^46	0.632727639
47	(1/1.01)^47	0.626463009
48	(1/1.01)^48	0.620260405
49	(1/1.01)^49	0.614119213
50	(1/1.01)^50	0.608038825
51	(1/1.01)^51	0.602018638
52	(1/1.01)^52	0.596058058
53	(1/1.01)^53	0.590156493
54	(1/1.01)^54	0.584313359
55	(1/1.01)^55	0.578528078
56	(1/1.01)^56	0.572800078
57	(1/1.01)^57	0.56712879
58	(1/1.01)^58	0.561513653
59	(1/1.01)^59	0.555954112
60	(1/1.01)^60	0.550449616
61	(1/1.01)^61	0.54499962
62	(1/1.01)^62	0.539603584
63	(1/1.01)^63	0.534260974
64	(1/1.01)^64	0.528971262
65	(1/1.01)^65	0.523733922
66	(1/1.01)^66	0.518548438
67	(1/1.01)^67	0.513414295
68	(1/1.01)^68	0.508330985
69	(1/1.01)^69	0.503298005
70	(1/1.01)^70	0.498314857
71	(1/1.01)^71	0.493381046
72	(1/1.01)^72	0.488496085
73	(1/1.01)^73	0.48365949
74	(1/1.01)^74	0.478870782
75	(1/1.01)^75	0.474129488
76	(1/1.01)^76	0.469435136
77	(1/1.01)^77	0.464787264
78	(1/1.01)^78	0.46018541
79	(1/1.01)^79	0.455629118
80	(1/1.01)^80	0.451117939
81	(1/1.01)^81	0.446651425
82	(1/1.01)^82	0.442229133
83	(1/1.01)^83	0.437850627
84	(1/1.01)^84	0.433515472
85	(1/1.01)^85	0.42922324
86	(1/1.01)^86	0.424973505
87	(1/1.01)^87	0.420765846
88	(1/1.01)^88	0.416599848
89	(1/1.01)^89	0.412475097
90	(1/1.01)^90	0.408391185
91	(1/1.01)^91	0.404347708
92	(1/1.01)^92	0.400344265
93	(1/1.01)^93	0.396380461
94	(1/1.01)^94	0.392455902
95	(1/1.01)^95	0.3885702
96	(1/1.01)^96	0.38472297
97	(1/1.01)^97	0.380913832
98	(1/1.01)^98	0.377142408
99	(1/1.01)^99	0.373408324
100	(1/1.01)^100	0.369711212
101	(1/1.01)^101	0.366050705
102	(1/1.01)^102	0.362426441
103	(1/1.01)^103	0.35883806
104	(1/1.01)^104	0.355285208
105	(1/1.01)^105	0.351767533
106	(1/1.01)^106	0.348284686
107	(1/1.01)^107	0.344836323
108	(1/1.01)^108	0.341422102
109	(1/1.01)^109	0.338041685
110	(1/1.01)^110	0.334694738
111	(1/1.01)^111	0.331380928
112	(1/1.01)^112	0.328099929
113	(1/1.01)^113	0.324851415
114	(1/1.01)^114	0.321635064
115	(1/1.01)^115	0.318450559
116	(1/1.01)^116	0.315297583
117	(1/1.01)^117	0.312175825
118	(1/1.01)^118	0.309084975
119	(1/1.01)^119	0.306024727
120	(1/1.01)^120	0.30299478
Total		69.70052203

We know that the Present value of the Future cash outflows is equal to the loan amount

Let the Quarterly Repayment be X

X * PVAF( 1% ,120) = $ 600000

X * 69.70052 = $ 600000

X = $ 600000/69.70052

X = $ 8608.257

Hence the Quarterly payment is $ 8608.26.So Option d is Correct.

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