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1 The sale of a house calls for payments of P950 at the end of each month for 25 years,if money is worth 18%, m= 12 what single payment today is equally acceptable?

2 A commercial bank pays interest at 13%, m= 2 on all the time deposits,what sequence of equal deposits at the end each six months for 5 years would accumulate for p120,000?

3 To provide for his daughter”s college educations, a man deposits P2,000 at the end of each 3 month for 6 years ,if the money draws 9% interest converted quarterly , how much does the fund contain after 6 years?

4 A couple left an inheritance to thier 7 years old son an amount of p6,000 a year, the money was deposited in a bank which offers 8% , m=1 , if the first payment was made on the child’s 10th birthday and the last payment on his 21st birthday ,, what amount will the child receive after the last payment?

Question 1

In this particular question, the payment at the end of each month is $ 950 for a period which needs to be discounted considering a discount rate of 18/12 = 1.5% per month as shown in the table below.

Month	Payment Made ($)	Present Value ($)
1	950	935.96
2	950	922.13
3	950	908.50
4	950	895.08
5	950	881.85
6	950	868.82
7	950	855.98
8	950	843.33
9	950	830.86
10	950	818.58
11	950	806.49
12	950	794.57
13	950	782.83
14	950	771.26
15	950	759.86
16	950	748.63
17	950	737.57
18	950	726.67
19	950	715.93
20	950	705.35
21	950	694.92
22	950	684.65
23	950	674.54
24	950	664.57
25	950	654.75
26	950	645.07
27	950	635.54
28	950	626.14
29	950	616.89
30	950	607.77
31	950	598.79
32	950	589.94
33	950	581.22
34	950	572.64
35	950	564.17
36	950	555.84
37	950	547.62
38	950	539.53
39	950	531.55
40	950	523.70
41	950	515.96
42	950	508.33
43	950	500.82
44	950	493.42
45	950	486.13
46	950	478.95
47	950	471.87
48	950	464.89
49	950	458.02
50	950	451.25
51	950	444.59
52	950	438.02
53	950	431.54
54	950	425.16
55	950	418.88
56	950	412.69
57	950	406.59
58	950	400.58
59	950	394.66
60	950	388.83
61	950	383.08
62	950	377.42
63	950	371.85
64	950	366.35
65	950	360.94
66	950	355.60
67	950	350.35
68	950	345.17
69	950	340.07
70	950	335.04
71	950	330.09
72	950	325.21
73	950	320.41
74	950	315.67
75	950	311.01
76	950	306.41
77	950	301.88
78	950	297.42
79	950	293.03
80	950	288.70
81	950	284.43
82	950	280.23
83	950	276.08
84	950	272.00
85	950	267.98
86	950	264.02
87	950	260.12
88	950	256.28
89	950	252.49
90	950	248.76
91	950	245.08
92	950	241.46
93	950	237.89
94	950	234.38
95	950	230.91
96	950	227.50
97	950	224.14
98	950	220.83
99	950	217.56
100	950	214.35
101	950	211.18
102	950	208.06
103	950	204.98
104	950	201.96
105	950	198.97
106	950	196.03
107	950	193.13
108	950	190.28
109	950	187.47
110	950	184.70
111	950	181.97
112	950	179.28
113	950	176.63
114	950	174.02
115	950	171.45
116	950	168.91
117	950	166.42
118	950	163.96
119	950	161.53
120	950	159.15
121	950	156.80
122	950	154.48
123	950	152.20
124	950	149.95
125	950	147.73
126	950	145.55
127	950	143.40
128	950	141.28
129	950	139.19
130	950	137.13
131	950	135.11
132	950	133.11
133	950	131.14
134	950	129.20
135	950	127.29
136	950	125.41
137	950	123.56
138	950	121.73
139	950	119.93
140	950	118.16
141	950	116.42
142	950	114.70
143	950	113.00
144	950	111.33
145	950	109.69
146	950	108.06
147	950	106.47
148	950	104.89
149	950	103.34
150	950	101.82
151	950	100.31
152	950	98.83
153	950	97.37
154	950	95.93
155	950	94.51
156	950	93.12
157	950	91.74
158	950	90.38
159	950	89.05
160	950	87.73
161	950	86.44
162	950	85.16
163	950	83.90
164	950	82.66
165	950	81.44
166	950	80.23
167	950	79.05
168	950	77.88
169	950	76.73
170	950	75.60
171	950	74.48
172	950	73.38
173	950	72.29
174	950	71.22
175	950	70.17
176	950	69.14
177	950	68.11
178	950	67.11
179	950	66.12
180	950	65.14
181	950	64.18
182	950	63.23
183	950	62.29
184	950	61.37
185	950	60.47
186	950	59.57
187	950	58.69
188	950	57.82
189	950	56.97
190	950	56.13
191	950	55.30
192	950	54.48
193	950	53.68
194	950	52.88
195	950	52.10
196	950	51.33
197	950	50.57
198	950	49.82
199	950	49.09
200	950	48.36
201	950	47.65
202	950	46.94
203	950	46.25
204	950	45.57
205	950	44.89
206	950	44.23
207	950	43.58
208	950	42.93
209	950	42.30
210	950	41.67
211	950	41.06
212	950	40.45
213	950	39.85
214	950	39.26
215	950	38.68
216	950	38.11
217	950	37.55
218	950	36.99
219	950	36.45
220	950	35.91
221	950	35.38
222	950	34.85
223	950	34.34
224	950	33.83
225	950	33.33
226	950	32.84
227	950	32.35
228	950	31.88
229	950	31.41
230	950	30.94
231	950	30.48
232	950	30.03
233	950	29.59
234	950	29.15
235	950	28.72
236	950	28.30
237	950	27.88
238	950	27.47
239	950	27.06
240	950	26.66
241	950	26.27
242	950	25.88
243	950	25.50
244	950	25.12
245	950	24.75
246	950	24.38
247	950	24.02
248	950	23.67
249	950	23.32
250	950	22.97
251	950	22.63
252	950	22.30
253	950	21.97
254	950	21.64
255	950	21.32
256	950	21.01
257	950	20.70
258	950	20.39
259	950	20.09
260	950	19.79
261	950	19.50
262	950	19.21
263	950	18.93
264	950	18.65
265	950	18.37
266	950	18.10
267	950	17.84
268	950	17.57
269	950	17.31
270	950	17.06
271	950	16.80
272	950	16.56
273	950	16.31
274	950	16.07
275	950	15.83
276	950	15.60
277	950	15.37
278	950	15.14
279	950	14.92
280	950	14.70
281	950	14.48
282	950	14.27
283	950	14.06
284	950	13.85
285	950	13.64
286	950	13.44
287	950	13.24
288	950	13.05
289	950	12.85
290	950	12.66
291	950	12.48
292	950	12.29
293	950	12.11
294	950	11.93
295	950	11.76
296	950	11.58
297	950	11.41
298	950	11.24
299	950	11.08
300	950	10.91
Total		62,605.86

Hence the equivalent payment which can be made today is $ 62,606 approximately.

Question 2

Rate of interest = 13% pa or 6.5% for six months

Here we need to find the FV factor for the various payments which are made of 6 months.

Half Year	Payment Made	Future Value
1	1	1.76
2	1	1.65
3	1	1.55
4	1	1.46
5	1	1.37
6	1	1.29
7	1	1.21
8	1	1.13
9	1	1.07
10	1	1.00
Total		13.4944

Let the equal payments made at the end of 6 months be $x

Then 13.4944 x = 120000

Hence x = $8,892.6 which can be rounded off to $8,893

Question 3

Money deposited after every 3 months = $ 2,000

Time period for which this is continued = 6 years

Interest rate = 9% pa = 2.25% per quarter

Hence the value of the fund at the end of the six years can be estimated as shown below.

Quarter	Payment Made	Future Value
1	2000	3336.46
2	2000	3263.04
3	2000	3191.24
4	2000	3121.02
5	2000	3052.34
6	2000	2985.17
7	2000	2919.49
8	2000	2855.24
9	2000	2792.41
10	2000	2730.97
11	2000	2670.87
12	2000	2612.10
13	2000	2554.62
14	2000	2498.41
15	2000	2443.43
16	2000	2389.66
17	2000	2337.08
18	2000	2285.65
19	2000	2235.36
20	2000	2186.17
21	2000	2138.06
22	2000	2091.01
23	2000	2045.00
24	2000	2000.00
Total		62,734.81

Hence the estimated value of the fund at the end of six years would be $ 62,735 approximately.

Question 4

Money received each year = $ 6,000

Applicable interest rate = 8% annually

The amount due at the 21^st birthday is calculated as shown below.

Birthday	Payment made	Value at 21st birthday
10	6000	13,989.83
11	6000	12,953.55
12	6000	11,994.03
13	6000	11,105.58
14	6000	10,282.95
15	6000	9,521.25
16	6000	8,815.97
17	6000	8,162.93
18	6000	7,558.27
19	6000	6,998.40
20	6000	6,480.00
21	6000	6,000.00
Total		113,862.76

Hence the amount received at 21^st birthday by the child would be $113,863 approximately.

Question 1

Question 2

Question 3

Question 4

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