Question

Assume you are 22 years old when you graduate from the University of Arizona and have a credit card of $2,000 credit balance with an 18% annual rate. If you only make minimun payments of 2% of the balance or just $10 (whichever is greater) each month , what birthday will you likely be celebrating when the credit card is paid off?

Answer 1

Solution:

Credit card balance at beginning = $2,000

Annual interest rate = 18%, monthly rate of interest = 18%/12 = 1.5%

monthly payment = 2% of balance or $10 whichever is higher.

Credit card repayment schedule
Monthly Period	Beginning balance	Interest Expense (1.5%)	Payment made (2% of balance or $10 whichever is higher)	Ending Balance
0				$2,000.00
1	$2,000.00	$30.00	$40.00	$1,990.00
2	$1,990.00	$29.85	$39.80	$1,980.05
3	$1,980.05	$29.70	$39.60	$1,970.15
4	$1,970.15	$29.55	$39.40	$1,960.30
5	$1,960.30	$29.40	$39.21	$1,950.50
6	$1,950.50	$29.26	$39.01	$1,940.75
7	$1,940.75	$29.11	$38.81	$1,931.04
8	$1,931.04	$28.97	$38.62	$1,921.39
9	$1,921.39	$28.82	$38.43	$1,911.78
10	$1,911.78	$28.68	$38.24	$1,902.22
11	$1,902.22	$28.53	$38.04	$1,892.71
12	$1,892.71	$28.39	$37.85	$1,883.25
13	$1,883.25	$28.25	$37.66	$1,873.83
14	$1,873.83	$28.11	$37.48	$1,864.46
15	$1,864.46	$27.97	$37.29	$1,855.14
16	$1,855.14	$27.83	$37.10	$1,845.86
17	$1,845.86	$27.69	$36.92	$1,836.63
18	$1,836.63	$27.55	$36.73	$1,827.45
19	$1,827.45	$27.41	$36.55	$1,818.31
20	$1,818.31	$27.27	$36.37	$1,809.22
21	$1,809.22	$27.14	$36.18	$1,800.17
22	$1,800.17	$27.00	$36.00	$1,791.17
23	$1,791.17	$26.87	$35.82	$1,782.22
24	$1,782.22	$26.73	$35.64	$1,773.31
25	$1,773.31	$26.60	$35.47	$1,764.44
26	$1,764.44	$26.47	$35.29	$1,755.62
27	$1,755.62	$26.33	$35.11	$1,746.84
28	$1,746.84	$26.20	$34.94	$1,738.11
29	$1,738.11	$26.07	$34.76	$1,729.42
30	$1,729.42	$25.94	$34.59	$1,720.77
31	$1,720.77	$25.81	$34.42	$1,712.16
32	$1,712.16	$25.68	$34.24	$1,703.60
33	$1,703.60	$25.55	$34.07	$1,695.09
34	$1,695.09	$25.43	$33.90	$1,686.61
35	$1,686.61	$25.30	$33.73	$1,678.18
36	$1,678.18	$25.17	$33.56	$1,669.79
37	$1,669.79	$25.05	$33.40	$1,661.44
38	$1,661.44	$24.92	$33.23	$1,653.13
39	$1,653.13	$24.80	$33.06	$1,644.86
40	$1,644.86	$24.67	$32.90	$1,636.64
41	$1,636.64	$24.55	$32.73	$1,628.46
42	$1,628.46	$24.43	$32.57	$1,620.31
43	$1,620.31	$24.30	$32.41	$1,612.21
44	$1,612.21	$24.18	$32.24	$1,604.15
45	$1,604.15	$24.06	$32.08	$1,596.13
46	$1,596.13	$23.94	$31.92	$1,588.15
47	$1,588.15	$23.82	$31.76	$1,580.21
48	$1,580.21	$23.70	$31.60	$1,572.31
49	$1,572.31	$23.58	$31.45	$1,564.45
50	$1,564.45	$23.47	$31.29	$1,556.63
51	$1,556.63	$23.35	$31.13	$1,548.84
52	$1,548.84	$23.23	$30.98	$1,541.10
53	$1,541.10	$23.12	$30.82	$1,533.39
54	$1,533.39	$23.00	$30.67	$1,525.73
55	$1,525.73	$22.89	$30.51	$1,518.10
56	$1,518.10	$22.77	$30.36	$1,510.51
57	$1,510.51	$22.66	$30.21	$1,502.95
58	$1,502.95	$22.54	$30.06	$1,495.44
59	$1,495.44	$22.43	$29.91	$1,487.96
60	$1,487.96	$22.32	$29.76	$1,480.52
61	$1,480.52	$22.21	$29.61	$1,473.12
62	$1,473.12	$22.10	$29.46	$1,465.75
63	$1,465.75	$21.99	$29.32	$1,458.42
64	$1,458.42	$21.88	$29.17	$1,451.13
65	$1,451.13	$21.77	$29.02	$1,443.88
66	$1,443.88	$21.66	$28.88	$1,436.66
67	$1,436.66	$21.55	$28.73	$1,429.47
68	$1,429.47	$21.44	$28.59	$1,422.33
69	$1,422.33	$21.33	$28.45	$1,415.22
70	$1,415.22	$21.23	$28.30	$1,408.14
71	$1,408.14	$21.12	$28.16	$1,401.10
72	$1,401.10	$21.02	$28.02	$1,394.09
73	$1,394.09	$20.91	$27.88	$1,387.12
74	$1,387.12	$20.81	$27.74	$1,380.19
75	$1,380.19	$20.70	$27.60	$1,373.29
76	$1,373.29	$20.60	$27.47	$1,366.42
77	$1,366.42	$20.50	$27.33	$1,359.59
78	$1,359.59	$20.39	$27.19	$1,352.79
79	$1,352.79	$20.29	$27.06	$1,346.03
80	$1,346.03	$20.19	$26.92	$1,339.30
81	$1,339.30	$20.09	$26.79	$1,332.60
82	$1,332.60	$19.99	$26.65	$1,325.94
83	$1,325.94	$19.89	$26.52	$1,319.31
84	$1,319.31	$19.79	$26.39	$1,312.71
85	$1,312.71	$19.69	$26.25	$1,306.15
86	$1,306.15	$19.59	$26.12	$1,299.62
87	$1,299.62	$19.49	$25.99	$1,293.12
88	$1,293.12	$19.40	$25.86	$1,286.65
89	$1,286.65	$19.30	$25.73	$1,280.22
90	$1,280.22	$19.20	$25.60	$1,273.82
91	$1,273.82	$19.11	$25.48	$1,267.45
92	$1,267.45	$19.01	$25.35	$1,261.11
93	$1,261.11	$18.92	$25.22	$1,254.81
94	$1,254.81	$18.82	$25.10	$1,248.53
95	$1,248.53	$18.73	$24.97	$1,242.29
96	$1,242.29	$18.63	$24.85	$1,236.08
97	$1,236.08	$18.54	$24.72	$1,229.90
98	$1,229.90	$18.45	$24.60	$1,223.75
99	$1,223.75	$18.36	$24.47	$1,217.63
100	$1,217.63	$18.26	$24.35	$1,211.54
101	$1,211.54	$18.17	$24.23	$1,205.48
102	$1,205.48	$18.08	$24.11	$1,199.46
103	$1,199.46	$17.99	$23.99	$1,193.46
104	$1,193.46	$17.90	$23.87	$1,187.49
105	$1,187.49	$17.81	$23.75	$1,181.55
106	$1,181.55	$17.72	$23.63	$1,175.65
107	$1,175.65	$17.63	$23.51	$1,169.77
108	$1,169.77	$17.55	$23.40	$1,163.92
109	$1,163.92	$17.46	$23.28	$1,158.10
110	$1,158.10	$17.37	$23.16	$1,152.31
111	$1,152.31	$17.28	$23.05	$1,146.55
112	$1,146.55	$17.20	$22.93	$1,140.81
113	$1,140.81	$17.11	$22.82	$1,135.11
114	$1,135.11	$17.03	$22.70	$1,129.43
115	$1,129.43	$16.94	$22.59	$1,123.79
116	$1,123.79	$16.86	$22.48	$1,118.17
117	$1,118.17	$16.77	$22.36	$1,112.58
118	$1,112.58	$16.69	$22.25	$1,107.02
119	$1,107.02	$16.61	$22.14	$1,101.48
120	$1,101.48	$16.52	$22.03	$1,095.97
121	$1,095.97	$16.44	$21.92	$1,090.49
122	$1,090.49	$16.36	$21.81	$1,085.04
123	$1,085.04	$16.28	$21.70	$1,079.62
124	$1,079.62	$16.19	$21.59	$1,074.22
125	$1,074.22	$16.11	$21.48	$1,068.85
126	$1,068.85	$16.03	$21.38	$1,063.50
127	$1,063.50	$15.95	$21.27	$1,058.18
128	$1,058.18	$15.87	$21.16	$1,052.89
129	$1,052.89	$15.79	$21.06	$1,047.63
130	$1,047.63	$15.71	$20.95	$1,042.39
131	$1,042.39	$15.64	$20.85	$1,037.18
132	$1,037.18	$15.56	$20.74	$1,031.99
133	$1,031.99	$15.48	$20.64	$1,026.83
134	$1,026.83	$15.40	$20.54	$1,021.70
135	$1,021.70	$15.33	$20.43	$1,016.59
136	$1,016.59	$15.25	$20.33	$1,011.51
137	$1,011.51	$15.17	$20.23	$1,006.45
138	$1,006.45	$15.10	$20.13	$1,001.42
139	$1,001.42	$15.02	$20.03	$996.41
140	$996.41	$14.95	$19.93	$991.43
141	$991.43	$14.87	$19.83	$986.47
142	$986.47	$14.80	$19.73	$981.54
143	$981.54	$14.72	$19.63	$976.63
144	$976.63	$14.65	$19.53	$971.75
145	$971.75	$14.58	$19.43	$966.89
146	$966.89	$14.50	$19.34	$962.05
147	$962.05	$14.43	$19.24	$957.24
148	$957.24	$14.36	$19.14	$952.46
149	$952.46	$14.29	$19.05	$947.70
150	$947.70	$14.22	$18.95	$942.96
151	$942.96	$14.14	$18.86	$938.24
152	$938.24	$14.07	$18.76	$933.55
153	$933.55	$14.00	$18.67	$928.88
154	$928.88	$13.93	$18.58	$924.24
155	$924.24	$13.86	$18.48	$919.62
156	$919.62	$13.79	$18.39	$915.02
157	$915.02	$13.73	$18.30	$910.44
158	$910.44	$13.66	$18.21	$905.89
159	$905.89	$13.59	$18.12	$901.36
160	$901.36	$13.52	$18.03	$896.86
161	$896.86	$13.45	$17.94	$892.37
162	$892.37	$13.39	$17.85	$887.91
163	$887.91	$13.32	$17.76	$883.47
164	$883.47	$13.25	$17.67	$879.05
165	$879.05	$13.19	$17.58	$874.66
166	$874.66	$13.12	$17.49	$870.28
167	$870.28	$13.05	$17.41	$865.93
168	$865.93	$12.99	$17.32	$861.60
169	$861.60	$12.92	$17.23	$857.30
170	$857.30	$12.86	$17.15	$853.01
171	$853.01	$12.80	$17.06	$848.74
172	$848.74	$12.73	$16.97	$844.50
173	$844.50	$12.67	$16.89	$840.28
174	$840.28	$12.60	$16.81	$836.08
175	$836.08	$12.54	$16.72	$831.90
176	$831.90	$12.48	$16.64	$827.74
177	$827.74	$12.42	$16.55	$823.60
178	$823.60	$12.35	$16.47	$819.48
179	$819.48	$12.29	$16.39	$815.38
180	$815.38	$12.23	$16.31	$811.31
181	$811.31	$12.17	$16.23	$807.25
182	$807.25	$12.11	$16.14	$803.21
183	$803.21	$12.05	$16.06	$799.20
184	$799.20	$11.99	$15.98	$795.20
185	$795.20	$11.93	$15.90	$791.22
186	$791.22	$11.87	$15.82	$787.27
187	$787.27	$11.81	$15.75	$783.33
188	$783.33	$11.75	$15.67	$779.42
189	$779.42	$11.69	$15.59	$775.52
190	$775.52	$11.63	$15.51	$771.64
191	$771.64	$11.57	$15.43	$767.78
192	$767.78	$11.52	$15.36	$763.94
193	$763.94	$11.46	$15.28	$760.12
194	$760.12	$11.40	$15.20	$756.32
195	$756.32	$11.34	$15.13	$752.54
196	$752.54	$11.29	$15.05	$748.78
197	$748.78	$11.23	$14.98	$745.04
198	$745.04	$11.18	$14.90	$741.31
199	$741.31	$11.12	$14.83	$737.60
200	$737.60	$11.06	$14.75	$733.92
201	$733.92	$11.01	$14.68	$730.25
202	$730.25	$10.95	$14.60	$726.59
203	$726.59	$10.90	$14.53	$722.96
204	$722.96	$10.84	$14.46	$719.35
205	$719.35	$10.79	$14.39	$715.75
206	$715.75	$10.74	$14.32	$712.17
207	$712.17	$10.68	$14.24	$708.61
208	$708.61	$10.63	$14.17	$705.07
209	$705.07	$10.58	$14.10	$701.54
210	$701.54	$10.52	$14.03	$698.03
211	$698.03	$10.47	$13.96	$694.54
212	$694.54	$10.42	$13.89	$691.07
213	$691.07	$10.37	$13.82	$687.62
214	$687.62	$10.31	$13.75	$684.18
215	$684.18	$10.26	$13.68	$680.76
216	$680.76	$10.21	$13.62	$677.35
217	$677.35	$10.16	$13.55	$673.97
218	$673.97	$10.11	$13.48	$670.60
219	$670.60	$10.06	$13.41	$667.24
220	$667.24	$10.01	$13.34	$663.91
221	$663.91	$9.96	$13.28	$660.59
222	$660.59	$9.91	$13.21	$657.29
223	$657.29	$9.86	$13.15	$654.00
224	$654.00	$9.81	$13.08	$650.73
225	$650.73	$9.76	$13.01	$647.48
226	$647.48	$9.71	$12.95	$644.24
227	$644.24	$9.66	$12.88	$641.02
228	$641.02	$9.62	$12.82	$637.81
229	$637.81	$9.57	$12.76	$634.62
230	$634.62	$9.52	$12.69	$631.45
231	$631.45	$9.47	$12.63	$628.29
232	$628.29	$9.42	$12.57	$625.15
233	$625.15	$9.38	$12.50	$622.02
234	$622.02	$9.33	$12.44	$618.91
235	$618.91	$9.28	$12.38	$615.82
236	$615.82	$9.24	$12.32	$612.74
237	$612.74	$9.19	$12.25	$609.68
238	$609.68	$9.15	$12.19	$606.63
239	$606.63	$9.10	$12.13	$603.60
240	$603.60	$9.05	$12.07	$600.58
241	$600.58	$9.01	$12.01	$597.58
242	$597.58	$8.96	$11.95	$594.59
243	$594.59	$8.92	$11.89	$591.61
244	$591.61	$8.87	$11.83	$588.66
245	$588.66	$8.83	$11.77	$585.71
246	$585.71	$8.79	$11.71	$582.78
247	$582.78	$8.74	$11.66	$579.87
248	$579.87	$8.70	$11.60	$576.97
249	$576.97	$8.65	$11.54	$574.09
250	$574.09	$8.61	$11.48	$571.22
251	$571.22	$8.57	$11.42	$568.36
252	$568.36	$8.53	$11.37	$565.52
253	$565.52	$8.48	$11.31	$562.69
254	$562.69	$8.44	$11.25	$559.88
255	$559.88	$8.40	$11.20	$557.08
256	$557.08	$8.36	$11.14	$554.29
257	$554.29	$8.31	$11.09	$551.52
258	$551.52	$8.27	$11.03	$548.76
259	$548.76	$8.23	$10.98	$546.02
260	$546.02	$8.19	$10.92	$543.29
261	$543.29	$8.15	$10.87	$540.57
262	$540.57	$8.11	$10.81	$537.87
263	$537.87	$8.07	$10.76	$535.18
264	$535.18	$8.03	$10.70	$532.50
265	$532.50	$7.99	$10.65	$529.84
266	$529.84	$7.95	$10.60	$527.19
267	$527.19	$7.91	$10.54	$524.56
268	$524.56	$7.87	$10.49	$521.93
269	$521.93	$7.83	$10.44	$519.32
270	$519.32	$7.79	$10.39	$516.73
271	$516.73	$7.75	$10.33	$514.14
272	$514.14	$7.71	$10.28	$511.57
273	$511.57	$7.67	$10.23	$509.02
274	$509.02	$7.64	$10.18	$506.47
275	$506.47	$7.60	$10.13	$503.94
276	$503.94	$7.56	$10.08	$501.42
277	$501.42	$7.52	$10.03	$498.91
278	$498.91	$7.48	$10.00	$496.39
279	$496.39	$7.45	$10.00	$493.84
280	$493.84	$7.41	$10.00	$491.25
281	$491.25	$7.37	$10.00	$488.62
282	$488.62	$7.33	$10.00	$485.95
283	$485.95	$7.29	$10.00	$483.24
284	$483.24	$7.25	$10.00	$480.48
285	$480.48	$7.21	$10.00	$477.69
286	$477.69	$7.17	$10.00	$474.86
287	$474.86	$7.12	$10.00	$471.98
288	$471.98	$7.08	$10.00	$469.06
289	$469.06	$7.04	$10.00	$466.10
290	$466.10	$6.99	$10.00	$463.09
291	$463.09	$6.95	$10.00	$460.03
292	$460.03	$6.90	$10.00	$456.93
293	$456.93	$6.85	$10.00	$453.79
294	$453.79	$6.81	$10.00	$450.59
295	$450.59	$6.76	$10.00	$447.35
296	$447.35	$6.71	$10.00	$444.06
297	$444.06	$6.66	$10.00	$440.72
298	$440.72	$6.61	$10.00	$437.34
299	$437.34	$6.56	$10.00	$433.90
300	$433.90	$6.51	$10.00	$430.40
301	$430.40	$6.46	$10.00	$426.86
302	$426.86	$6.40	$10.00	$423.26
303	$423.26	$6.35	$10.00	$419.61
304	$419.61	$6.29	$10.00	$415.91
305	$415.91	$6.24	$10.00	$412.14
306	$412.14	$6.18	$10.00	$408.33
307	$408.33	$6.12	$10.00	$404.45
308	$404.45	$6.07	$10.00	$400.52
309	$400.52	$6.01	$10.00	$396.53
310	$396.53	$5.95	$10.00	$392.47
311	$392.47	$5.89	$10.00	$388.36
312	$388.36	$5.83	$10.00	$384.19
313	$384.19	$5.76	$10.00	$379.95
314	$379.95	$5.70	$10.00	$375.65
315	$375.65	$5.63	$10.00	$371.28
316	$371.28	$5.57	$10.00	$366.85
317	$366.85	$5.50	$10.00	$362.36
318	$362.36	$5.44	$10.00	$357.79
319	$357.79	$5.37	$10.00	$353.16
320	$353.16	$5.30	$10.00	$348.45
321	$348.45	$5.23	$10.00	$343.68
322	$343.68	$5.16	$10.00	$338.84
323	$338.84	$5.08	$10.00	$333.92
324	$333.92	$5.01	$10.00	$328.93
325	$328.93	$4.93	$10.00	$323.86
326	$323.86	$4.86	$10.00	$318.72
327	$318.72	$4.78	$10.00	$313.50
328	$313.50	$4.70	$10.00	$308.20
329	$308.20	$4.62	$10.00	$302.83
330	$302.83	$4.54	$10.00	$297.37
331	$297.37	$4.46	$10.00	$291.83
332	$291.83	$4.38	$10.00	$286.21
333	$286.21	$4.29	$10.00	$280.50
334	$280.50	$4.21	$10.00	$274.71
335	$274.71	$4.12	$10.00	$268.83
336	$268.83	$4.03	$10.00	$262.86
337	$262.86	$3.94	$10.00	$256.80
338	$256.80	$3.85	$10.00	$250.66
339	$250.66	$3.76	$10.00	$244.42
340	$244.42	$3.67	$10.00	$238.08
341	$238.08	$3.57	$10.00	$231.65
342	$231.65	$3.47	$10.00	$225.13
343	$225.13	$3.38	$10.00	$218.50
344	$218.50	$3.28	$10.00	$211.78
345	$211.78	$3.18	$10.00	$204.96
346	$204.96	$3.07	$10.00	$198.03
347	$198.03	$2.97	$10.00	$191.00
348	$191.00	$2.87	$10.00	$183.87
349	$183.87	$2.76	$10.00	$176.63
350	$176.63	$2.65	$10.00	$169.28
351	$169.28	$2.54	$10.00	$161.82
352	$161.82	$2.43	$10.00	$154.24
353	$154.24	$2.31	$10.00	$146.56
354	$146.56	$2.20	$10.00	$138.75
355	$138.75	$2.08	$10.00	$130.84
356	$130.84	$1.96	$10.00	$122.80
357	$122.80	$1.84	$10.00	$114.64
358	$114.64	$1.72	$10.00	$106.36
359	$106.36	$1.60	$10.00	$97.96
360	$97.96	$1.47	$10.00	$89.42
361	$89.42	$1.34	$10.00	$80.77
362	$80.77	$1.21	$10.00	$71.98
363	$71.98	$1.08	$10.00	$63.06
364	$63.06	$0.95	$10.00	$54.00
365	$54.00	$0.81	$10.00	$44.81
366	$44.81	$0.67	$10.00	$35.49
367	$35.49	$0.53	$10.00	$26.02
368	$26.02	$0.39	$10.00	$16.41
369	$16.41	$0.25	$10.00	$6.65
370	$6.65	$0.10	$6.75	$0.00

It will take 370 months to make credit card payments, it means almost 31 years (rounded off from 30.83 years). Therefore i will be celebrating by 53 rd birthday (31+ 22) when credit card is paid off.