Question

This financial option is offered by a university for its degree course that lasts exactly three years.

The students will repay in instalments after the end of the course. The instalments are determined as follows:

• No payments are made until three years after the end of the course.

• Over the following 15 years, students pay the university RM325 at the beginning of each quarter.

• After 15 years of payments, the quarterly instalments are increased to RM375 at the beginning of each quarter.

• After a further 15 years of payments, the quarterly instalments are increased to RM450 at the beginning of each quarter for a further 15-year period after which there are no more payments.

The rate of interest is at 3% per annum effective.

Calculate the present value.

Answer 1

The frist instalemet will be paid at the start of 7th year (ie at the end of 6th year which is quarter 24th)

Instalment of 325 will be paid from Quarter (24-83)

Instalment of 375 will be paid from Quarter (84-143)

Instalment of 450 will be paid from Quarter (144-203)

First of all we will calculate the quarterly nominal discount rate

Nominal rate = (1.03)^(1/4) = 0.7417% per quarter

Quarter	Amount	Present value factor @ 0.7417% per quarter	Present Value
24	325	0.84	272.18
25	325	0.83	270.18
26	325	0.83	268.19
27	325	0.82	266.22
28	325	0.81	264.26
29	325	0.81	262.31
30	325	0.80	260.38
31	325	0.80	258.46
32	325	0.79	256.56
33	325	0.78	254.67
34	325	0.78	252.79
35	325	0.77	250.93
36	325	0.77	249.09
37	325	0.76	247.25
38	325	0.76	245.43
39	325	0.75	243.62
40	325	0.74	241.83
41	325	0.74	240.05
42	325	0.73	238.28
43	325	0.73	236.53
44	325	0.72	234.79
45	325	0.72	233.06
46	325	0.71	231.34
47	325	0.71	229.64
48	325	0.70	227.95
49	325	0.70	226.27
50	325	0.69	224.61
51	325	0.69	222.95
52	325	0.68	221.31
53	325	0.68	219.68
54	325	0.67	218.06
55	325	0.67	216.46
56	325	0.66	214.86
57	325	0.66	213.28
58	325	0.65	211.71
59	325	0.65	210.15
60	325	0.64	208.61
61	325	0.64	207.07
62	325	0.63	205.55
63	325	0.63	204.03
64	325	0.62	202.53
65	325	0.62	201.04
66	325	0.61	199.56
67	325	0.61	198.09
68	325	0.61	196.63
69	325	0.60	195.18
70	325	0.60	193.75
71	325	0.59	192.32
72	325	0.59	190.90
73	325	0.58	189.50
74	325	0.58	188.10
75	325	0.57	186.72
76	325	0.57	185.34
77	325	0.57	183.98
78	325	0.56	182.62
79	325	0.56	181.28
80	325	0.55	179.95
81	325	0.55	178.62
82	325	0.55	177.31
83	325	0.54	176.00
84	375	0.54	201.58
85	375	0.53	200.10
86	375	0.53	198.62
87	375	0.53	197.16
88	375	0.52	195.71
89	375	0.52	194.27
90	375	0.51	192.84
91	375	0.51	191.42
92	375	0.51	190.01
93	375	0.50	188.61
94	375	0.50	187.22
95	375	0.50	185.84
96	375	0.49	184.48
97	375	0.49	183.12
98	375	0.48	181.77
99	375	0.48	180.43
100	375	0.48	179.10
101	375	0.47	177.78
102	375	0.47	176.48
103	375	0.47	175.18
104	375	0.46	173.89
105	375	0.46	172.61
106	375	0.46	171.34
107	375	0.45	170.07
108	375	0.45	168.82
109	375	0.45	167.58
110	375	0.44	166.35
111	375	0.44	165.12
112	375	0.44	163.91
113	375	0.43	162.70
114	375	0.43	161.50
115	375	0.43	160.31
116	375	0.42	159.13
117	375	0.42	157.96
118	375	0.42	156.80
119	375	0.42	155.64
120	375	0.41	154.50
121	375	0.41	153.36
122	375	0.41	152.23
123	375	0.40	151.11
124	375	0.40	150.00
125	375	0.40	148.89
126	375	0.39	147.80
127	375	0.39	146.71
128	375	0.39	145.63
129	375	0.39	144.56
130	375	0.38	143.49
131	375	0.38	142.43
132	375	0.38	141.39
133	375	0.37	140.35
134	375	0.37	139.31
135	375	0.37	138.29
136	375	0.37	137.27
137	375	0.36	136.26
138	375	0.36	135.25
139	375	0.36	134.26
140	375	0.36	133.27
141	375	0.35	132.29
142	375	0.35	131.31
143	375	0.35	130.35
144	450	0.35	155.27
145	450	0.34	154.12
146	450	0.34	152.99
147	450	0.34	151.86
148	450	0.33	150.74
149	450	0.33	149.63
150	450	0.33	148.53
151	450	0.33	147.44
152	450	0.33	146.35
153	450	0.32	145.28
154	450	0.32	144.21
155	450	0.32	143.14
156	450	0.32	142.09
157	450	0.31	141.04
158	450	0.31	140.01
159	450	0.31	138.98
160	450	0.31	137.95
161	450	0.30	136.94
162	450	0.30	135.93
163	450	0.30	134.93
164	450	0.30	133.93
165	450	0.30	132.95
166	450	0.29	131.97
167	450	0.29	131.00
168	450	0.29	130.03
169	450	0.29	129.08
170	450	0.28	128.13
171	450	0.28	127.18
172	450	0.28	126.25
173	450	0.28	125.32
174	450	0.28	124.39
175	450	0.27	123.48
176	450	0.27	122.57
177	450	0.27	121.67
178	450	0.27	120.77
179	450	0.27	119.88
180	450	0.26	119.00
181	450	0.26	118.12
182	450	0.26	117.25
183	450	0.26	116.39
184	450	0.26	115.53
185	450	0.25	114.68
186	450	0.25	113.84
187	450	0.25	113.00
188	450	0.25	112.17
189	450	0.25	111.34
190	450	0.25	110.52
191	450	0.24	109.71
192	450	0.24	108.90
193	450	0.24	108.10
194	450	0.24	107.30
195	450	0.24	106.51
196	450	0.23	105.73
197	450	0.23	104.95
198	450	0.23	104.18
199	450	0.23	103.41
200	450	0.23	102.65
201	450	0.23	101.89
202	450	0.22	101.14
203	450	0.22	100.40
		Present Value of the loan	30,598.51