Question

A gradient payment series is received monthly for 20 years and deposited into an account. The first payment is $2,000 and the gradient factor is $100 per month. What is the balance in the account after the initial 20 years? AFTER the first 20 years, the gradient factor is then doubled for an additional 10 years. At an interest rate of 6% compounded monthly (throughout the 30 years). What is the balance in the account after the last payment is deposited at the end of the 30th year?

Answer 1

THIS CAN BE SOLVED IN EXCEL AS FOLLOWS:

THE CASHFLOWS ARE:

1	2,000.00
2	2,100.00
3	2,200.00
4	2,300.00
5	2,400.00
6	2,500.00
7	2,600.00
8	2,700.00
9	2,800.00
10	2,900.00
11	3,000.00
12	3,100.00
13	3,200.00
14	3,300.00
15	3,400.00
16	3,500.00
17	3,600.00
18	3,700.00
19	3,800.00
20	3,900.00
21	4,000.00
22	4,100.00
23	4,200.00
24	4,300.00
25	4,400.00
26	4,500.00
27	4,600.00
28	4,700.00
29	4,800.00
30	4,900.00
31	5,000.00
32	5,100.00
33	5,200.00
34	5,300.00
35	5,400.00
36	5,500.00
37	5,600.00
38	5,700.00
39	5,800.00
40	5,900.00
41	6,000.00
42	6,100.00
43	6,200.00
44	6,300.00
45	6,400.00
46	6,500.00
47	6,600.00
48	6,700.00
49	6,800.00
50	6,900.00
51	7,000.00
52	7,100.00
53	7,200.00
54	7,300.00
55	7,400.00
56	7,500.00
57	7,600.00
58	7,700.00
59	7,800.00
60	7,900.00
61	8,000.00
62	8,100.00
63	8,200.00
64	8,300.00
65	8,400.00
66	8,500.00
67	8,600.00
68	8,700.00
69	8,800.00
70	8,900.00
71	9,000.00
72	9,100.00
73	9,200.00
74	9,300.00
75	9,400.00
76	9,500.00
77	9,600.00
78	9,700.00
79	9,800.00
80	9,900.00
81	10,000.00
82	10,100.00
83	10,200.00
84	10,300.00
85	10,400.00
86	10,500.00
87	10,600.00
88	10,700.00
89	10,800.00
90	10,900.00
91	11,000.00
92	11,100.00
93	11,200.00
94	11,300.00
95	11,400.00
96	11,500.00
97	11,600.00
98	11,700.00
99	11,800.00
100	11,900.00
101	12,000.00
102	12,100.00
103	12,200.00
104	12,300.00
105	12,400.00
106	12,500.00
107	12,600.00
108	12,700.00
109	12,800.00
110	12,900.00
111	13,000.00
112	13,100.00
113	13,200.00
114	13,300.00
115	13,400.00
116	13,500.00
117	13,600.00
118	13,700.00
119	13,800.00
120	13,900.00
121	14,000.00
122	14,100.00
123	14,200.00
124	14,300.00
125	14,400.00
126	14,500.00
127	14,600.00
128	14,700.00
129	14,800.00
130	14,900.00
131	15,000.00
132	15,100.00
133	15,200.00
134	15,300.00
135	15,400.00
136	15,500.00
137	15,600.00
138	15,700.00
139	15,800.00
140	15,900.00
141	16,000.00
142	16,100.00
143	16,200.00
144	16,300.00
145	16,400.00
146	16,500.00
147	16,600.00
148	16,700.00
149	16,800.00
150	16,900.00
151	17,000.00
152	17,100.00
153	17,200.00
154	17,300.00
155	17,400.00
156	17,500.00
157	17,600.00
158	17,700.00
159	17,800.00
160	17,900.00
161	18,000.00
162	18,100.00
163	18,200.00
164	18,300.00
165	18,400.00
166	18,500.00
167	18,600.00
168	18,700.00
169	18,800.00
170	18,900.00
171	19,000.00
172	19,100.00
173	19,200.00
174	19,300.00
175	19,400.00
176	19,500.00
177	19,600.00
178	19,700.00
179	19,800.00
180	19,900.00
181	20,000.00
182	20,100.00
183	20,200.00
184	20,300.00
185	20,400.00
186	20,500.00
187	20,600.00
188	20,700.00
189	20,800.00
190	20,900.00
191	21,000.00
192	21,100.00
193	21,200.00
194	21,300.00
195	21,400.00
196	21,500.00
197	21,600.00
198	21,700.00
199	21,800.00
200	21,900.00
201	22,000.00
202	22,100.00
203	22,200.00
204	22,300.00
205	22,400.00
206	22,500.00
207	22,600.00
208	22,700.00
209	22,800.00
210	22,900.00
211	23,000.00
212	23,100.00
213	23,200.00
214	23,300.00
215	23,400.00
216	23,500.00
217	23,600.00
218	23,700.00
219	23,800.00
220	23,900.00
221	24,000.00
222	24,100.00
223	24,200.00
224	24,300.00
225	24,400.00
226	24,500.00
227	24,600.00
228	24,700.00
229	24,800.00
230	24,900.00
231	25,000.00
232	25,100.00
233	25,200.00
234	25,300.00
235	25,400.00
236	25,500.00
237	25,600.00
238	25,700.00
239	25,800.00
240	25,900.00
241	26,100.00
242	26,300.00
243	26,500.00
244	26,700.00
245	26,900.00
246	27,100.00
247	27,300.00
248	27,500.00
249	27,700.00
250	27,900.00
251	28,100.00
252	28,300.00
253	28,500.00
254	28,700.00
255	28,900.00
256	29,100.00
257	29,300.00
258	29,500.00
259	29,700.00
260	29,900.00
261	30,100.00
262	30,300.00
263	30,500.00
264	30,700.00
265	30,900.00
266	31,100.00
267	31,300.00
268	31,500.00
269	31,700.00
270	31,900.00
271	32,100.00
272	32,300.00
273	32,500.00
274	32,700.00
275	32,900.00
276	33,100.00
277	33,300.00
278	33,500.00
279	33,700.00
280	33,900.00
281	34,100.00
282	34,300.00
283	34,500.00
284	34,700.00
285	34,900.00
286	35,100.00
287	35,300.00
288	35,500.00
289	35,700.00
290	35,900.00
291	36,100.00
292	36,300.00
293	36,500.00
294	36,700.00
295	36,900.00
296	37,100.00
297	37,300.00
298	37,500.00
299	37,700.00
300	37,900.00
301	38,100.00
302	38,300.00
303	38,500.00
304	38,700.00
305	38,900.00
306	39,100.00
307	39,300.00
308	39,500.00
309	39,700.00
310	39,900.00
311	40,100.00
312	40,300.00
313	40,500.00
314	40,700.00
315	40,900.00
316	41,100.00
317	41,300.00
318	41,500.00
319	41,700.00
320	41,900.00
321	42,100.00
322	42,300.00
323	42,500.00
324	42,700.00
325	42,900.00
326	43,100.00
327	43,300.00
328	43,500.00
329	43,700.00
330	43,900.00
331	44,100.00
332	44,300.00
333	44,500.00
334	44,700.00
335	44,900.00
336	45,100.00
337	45,300.00
338	45,500.00
339	45,700.00
340	45,900.00
341	46,100.00
342	46,300.00
343	46,500.00
344	46,700.00
345	46,900.00
346	47,100.00
347	47,300.00
348	47,500.00
349	47,700.00
350	47,900.00
351	48,100.00
352	48,300.00
353	48,500.00
354	48,700.00
355	48,900.00
356	49,100.00
357	49,300.00
358	49,500.00
359	49,700.00
360	49,900.00

BALANCE AFTER 20 YEARS= NPV(0.06/12,2000:25900)=1620715.50

BALANCE AFTER 30 YEARS=NPV(0.06/12,2000:49900)=2622350.95