Question

You have found three investments choices for one year deposit 9.3% APR, compounded, 9.3 APR compounded monthly, 9.3% compounded annaully, and 8.4% APR daily. Compute the EAR for investment choice. (365 days in a year).

Answer 1

Assume we are having $ 1000 invest:

i)9.3% APR Compounded Monthly

S.No	Opening Balance	Deposit amount	Interest@ 0.775%	Total
1		$1,000	7.75	$1,008
2	$1,008	$0	$7.81	$1,015.56
3	$1,016	$0	$7.87	$1,023.43
4	$1,023	$0	$7.93	$1,031.36
5	$1,031	$0	$7.99	$1,039.36
6	$1,039	$0	$8.06	$1,047.41
7	$1,047	$0	$8.12	$1,055.53
8	$1,056	$0	$8.18	$1,063.71
9	$1,064	$0	$8.24	$1,071.95
10	$1,072	$0	$8.31	$1,080.26
11	$1,080	$0	$8.37	$1,088.63
12	$1,089	$0	$8.44	$1,097.07

ROI p.a = 9.3%

Rate of interest per month = 9.3%/12=0.775%

Annual Return =( $ 1097.07-$ 1000)/$ 1000*100

= 9.7070%

ii)9.3% Compounded Annually:

Outstanding Amount = $ 1000*1.093

= $ 1093

Annual Return =( $ 1093-$ 1000)/$ 1000*100

= 9.3%

iii) 8.4% Compounded Annually

S.No	Opening Balance	Deposit amount	Interest@ 0.02301	Total
1	$0	$1,000	$0.23014	$1,000.23
2	$1,000.23	$0	$0.23015	$1,000.46
3	$1,000.46	$0	$0.23021	$1,000.69
4	$1,000.69	$0	$0.23026	$1,000.92
5	$1,000.92	$0	$0.23031	$1,001.15
6	$1,001.15	$0	$0.23036	$1,001.38
7	$1,001.38	$0	$0.23042	$1,001.61
8	$1,001.61	$0	$0.23047	$1,001.84
9	$1,001.84	$0	$0.23052	$1,002.07
10	$1,002.07	$0	$0.23058	$1,002.30
11	$1,002.30	$0	$0.23063	$1,002.53
12	$1,002.53	$0	$0.23068	$1,002.76
13	$1,002.76	$0	$0.23074	$1,003.00
14	$1,003.00	$0	$0.23079	$1,003.23
15	$1,003.23	$0	$0.23084	$1,003.46
16	$1,003.46	$0	$0.23090	$1,003.69
17	$1,003.69	$0	$0.23095	$1,003.92
18	$1,003.92	$0	$0.23100	$1,004.15
19	$1,004.15	$0	$0.23105	$1,004.38
20	$1,004.38	$0	$0.23111	$1,004.61
21	$1,004.61	$0	$0.23116	$1,004.84
22	$1,004.84	$0	$0.23121	$1,005.07
23	$1,005.07	$0	$0.23127	$1,005.31
24	$1,005.31	$0	$0.23132	$1,005.54
25	$1,005.54	$0	$0.23137	$1,005.77
26	$1,005.77	$0	$0.23143	$1,006.00
27	$1,006.00	$0	$0.23148	$1,006.23
28	$1,006.23	$0	$0.23153	$1,006.46
29	$1,006.46	$0	$0.23159	$1,006.69
30	$1,006.69	$0	$0.23164	$1,006.93
31	$1,006.93	$0	$0.23169	$1,007.16
32	$1,007.16	$0	$0.23175	$1,007.39
33	$1,007.39	$0	$0.23180	$1,007.62
34	$1,007.62	$0	$0.23185	$1,007.85
35	$1,007.85	$0	$0.23191	$1,008.09
36	$1,008.09	$0	$0.23196	$1,008.32
37	$1,008.32	$0	$0.23201	$1,008.55
38	$1,008.55	$0	$0.23207	$1,008.78
39	$1,008.78	$0	$0.23212	$1,009.01
40	$1,009.01	$0	$0.23217	$1,009.25
41	$1,009.25	$0	$0.23223	$1,009.48
42	$1,009.48	$0	$0.23228	$1,009.71
43	$1,009.71	$0	$0.23233	$1,009.94
44	$1,009.94	$0	$0.23239	$1,010.17
45	$1,010.17	$0	$0.23244	$1,010.41
46	$1,010.41	$0	$0.23249	$1,010.64
47	$1,010.64	$0	$0.23255	$1,010.87
48	$1,010.87	$0	$0.23260	$1,011.10
49	$1,011.10	$0	$0.23266	$1,011.34
50	$1,011.34	$0	$0.23271	$1,011.57
51	$1,011.57	$0	$0.23276	$1,011.80
52	$1,011.80	$0	$0.23282	$1,012.04
53	$1,012.04	$0	$0.23287	$1,012.27
54	$1,012.27	$0	$0.23292	$1,012.50
55	$1,012.50	$0	$0.23298	$1,012.73
56	$1,012.73	$0	$0.23303	$1,012.97
57	$1,012.97	$0	$0.23308	$1,013.20
58	$1,013.20	$0	$0.23314	$1,013.43
59	$1,013.43	$0	$0.23319	$1,013.67
60	$1,013.67	$0	$0.23324	$1,013.90
61	$1,013.90	$0	$0.23330	$1,014.13
62	$1,014.13	$0	$0.23335	$1,014.37
63	$1,014.37	$0	$0.23341	$1,014.60
64	$1,014.60	$0	$0.23346	$1,014.83
65	$1,014.83	$0	$0.23351	$1,015.07
66	$1,015.07	$0	$0.23357	$1,015.30
67	$1,015.30	$0	$0.23362	$1,015.53
68	$1,015.53	$0	$0.23367	$1,015.77
69	$1,015.77	$0	$0.23373	$1,016.00
70	$1,016.00	$0	$0.23378	$1,016.24
71	$1,016.24	$0	$0.23384	$1,016.47
72	$1,016.47	$0	$0.23389	$1,016.70
73	$1,016.70	$0	$0.23394	$1,016.94
74	$1,016.94	$0	$0.23400	$1,017.17
75	$1,017.17	$0	$0.23405	$1,017.41
76	$1,017.41	$0	$0.23410	$1,017.64
77	$1,017.64	$0	$0.23416	$1,017.87
78	$1,017.87	$0	$0.23421	$1,018.11
79	$1,018.11	$0	$0.23427	$1,018.34
80	$1,018.34	$0	$0.23432	$1,018.58
81	$1,018.58	$0	$0.23437	$1,018.81
82	$1,018.81	$0	$0.23443	$1,019.05
83	$1,019.05	$0	$0.23448	$1,019.28
84	$1,019.28	$0	$0.23454	$1,019.51
85	$1,019.51	$0	$0.23459	$1,019.75
86	$1,019.75	$0	$0.23464	$1,019.98
87	$1,019.98	$0	$0.23470	$1,020.22
88	$1,020.22	$0	$0.23475	$1,020.45
89	$1,020.45	$0	$0.23481	$1,020.69
90	$1,020.69	$0	$0.23486	$1,020.92
91	$1,020.92	$0	$0.23491	$1,021.16
92	$1,021.16	$0	$0.23497	$1,021.39
93	$1,021.39	$0	$0.23502	$1,021.63
94	$1,021.63	$0	$0.23508	$1,021.86
95	$1,021.86	$0	$0.23513	$1,022.10
96	$1,022.10	$0	$0.23518	$1,022.33
97	$1,022.33	$0	$0.23524	$1,022.57
98	$1,022.57	$0	$0.23529	$1,022.80
99	$1,022.80	$0	$0.23535	$1,023.04
100	$1,023.04	$0	$0.23540	$1,023.27
101	$1,023.27	$0	$0.23546	$1,023.51
102	$1,023.51	$0	$0.23551	$1,023.75
103	$1,023.75	$0	$0.23556	$1,023.98
104	$1,023.98	$0	$0.23562	$1,024.22
105	$1,024.22	$0	$0.23567	$1,024.45
106	$1,024.45	$0	$0.23573	$1,024.69
107	$1,024.69	$0	$0.23578	$1,024.92
108	$1,024.92	$0	$0.23583	$1,025.16
109	$1,025.16	$0	$0.23589	$1,025.40
110	$1,025.40	$0	$0.23594	$1,025.63
111	$1,025.63	$0	$0.23600	$1,025.87
112	$1,025.87	$0	$0.23605	$1,026.10
113	$1,026.10	$0	$0.23611	$1,026.34
114	$1,026.34	$0	$0.23616	$1,026.58
115	$1,026.58	$0	$0.23622	$1,026.81
116	$1,026.81	$0	$0.23627	$1,027.05
117	$1,027.05	$0	$0.23632	$1,027.28
118	$1,027.28	$0	$0.23638	$1,027.52
119	$1,027.52	$0	$0.23643	$1,027.76
120	$1,027.76	$0	$0.23649	$1,027.99
121	$1,027.99	$0	$0.23654	$1,028.23
122	$1,028.23	$0	$0.23660	$1,028.47
123	$1,028.47	$0	$0.23665	$1,028.70
124	$1,028.70	$0	$0.23670	$1,028.94
125	$1,028.94	$0	$0.23676	$1,029.18
126	$1,029.18	$0	$0.23681	$1,029.41
127	$1,029.41	$0	$0.23687	$1,029.65
128	$1,029.65	$0	$0.23692	$1,029.89
129	$1,029.89	$0	$0.23698	$1,030.12
130	$1,030.12	$0	$0.23703	$1,030.36
131	$1,030.36	$0	$0.23709	$1,030.60
132	$1,030.60	$0	$0.23714	$1,030.84
133	$1,030.84	$0	$0.23720	$1,031.07
134	$1,031.07	$0	$0.23725	$1,031.31
135	$1,031.31	$0	$0.23730	$1,031.55
136	$1,031.55	$0	$0.23736	$1,031.78
137	$1,031.78	$0	$0.23741	$1,032.02
138	$1,032.02	$0	$0.23747	$1,032.26
139	$1,032.26	$0	$0.23752	$1,032.50
140	$1,032.50	$0	$0.23758	$1,032.73
141	$1,032.73	$0	$0.23763	$1,032.97
142	$1,032.97	$0	$0.23769	$1,033.21
143	$1,033.21	$0	$0.23774	$1,033.45
144	$1,033.45	$0	$0.23780	$1,033.69
145	$1,033.69	$0	$0.23785	$1,033.92
146	$1,033.92	$0	$0.23791	$1,034.16
147	$1,034.16	$0	$0.23796	$1,034.40
148	$1,034.40	$0	$0.23802	$1,034.64
149	$1,034.64	$0	$0.23807	$1,034.88
150	$1,034.88	$0	$0.23812	$1,035.11
151	$1,035.11	$0	$0.23818	$1,035.35
152	$1,035.35	$0	$0.23823	$1,035.59
153	$1,035.59	$0	$0.23829	$1,035.83
154	$1,035.83	$0	$0.23834	$1,036.07
155	$1,036.07	$0	$0.23840	$1,036.30
156	$1,036.30	$0	$0.23845	$1,036.54
157	$1,036.54	$0	$0.23851	$1,036.78
158	$1,036.78	$0	$0.23856	$1,037.02
159	$1,037.02	$0	$0.23862	$1,037.26
160	$1,037.26	$0	$0.23867	$1,037.50
161	$1,037.50	$0	$0.23873	$1,037.74
162	$1,037.74	$0	$0.23878	$1,037.98
163	$1,037.98	$0	$0.23884	$1,038.21
164	$1,038.21	$0	$0.23889	$1,038.45
165	$1,038.45	$0	$0.23895	$1,038.69
166	$1,038.69	$0	$0.23900	$1,038.93
167	$1,038.93	$0	$0.23906	$1,039.17
168	$1,039.17	$0	$0.23911	$1,039.41
169	$1,039.41	$0	$0.23917	$1,039.65
170	$1,039.65	$0	$0.23922	$1,039.89
171	$1,039.89	$0	$0.23928	$1,040.13
172	$1,040.13	$0	$0.23933	$1,040.37
173	$1,040.37	$0	$0.23939	$1,040.61
174	$1,040.61	$0	$0.23944	$1,040.84
175	$1,040.84	$0	$0.23950	$1,041.08
176	$1,041.08	$0	$0.23955	$1,041.32
177	$1,041.32	$0	$0.23961	$1,041.56
178	$1,041.56	$0	$0.23966	$1,041.80
179	$1,041.80	$0	$0.23972	$1,042.04
180	$1,042.04	$0	$0.23977	$1,042.28
181	$1,042.28	$0	$0.23983	$1,042.52
182	$1,042.52	$0	$0.23988	$1,042.76
183	$1,042.76	$0	$0.23994	$1,043.00
184	$1,043.00	$0	$0.23999	$1,043.24
185	$1,043.24	$0	$0.24005	$1,043.48
186	$1,043.48	$0	$0.24011	$1,043.72
187	$1,043.72	$0	$0.24016	$1,043.96
188	$1,043.96	$0	$0.24022	$1,044.20
189	$1,044.20	$0	$0.24027	$1,044.44
190	$1,044.44	$0	$0.24033	$1,044.68
191	$1,044.68	$0	$0.24038	$1,044.92
192	$1,044.92	$0	$0.24044	$1,045.16
193	$1,045.16	$0	$0.24049	$1,045.40
194	$1,045.40	$0	$0.24055	$1,045.65
195	$1,045.65	$0	$0.24060	$1,045.89
196	$1,045.89	$0	$0.24066	$1,046.13
197	$1,046.13	$0	$0.24071	$1,046.37
198	$1,046.37	$0	$0.24077	$1,046.61
199	$1,046.61	$0	$0.24082	$1,046.85
200	$1,046.85	$0	$0.24088	$1,047.09
201	$1,047.09	$0	$0.24094	$1,047.33
202	$1,047.33	$0	$0.24099	$1,047.57
203	$1,047.57	$0	$0.24105	$1,047.81
204	$1,047.81	$0	$0.24110	$1,048.05
205	$1,048.05	$0	$0.24116	$1,048.30
206	$1,048.30	$0	$0.24121	$1,048.54
207	$1,048.54	$0	$0.24127	$1,048.78
208	$1,048.78	$0	$0.24132	$1,049.02
209	$1,049.02	$0	$0.24138	$1,049.26
210	$1,049.26	$0	$0.24143	$1,049.50
211	$1,049.50	$0	$0.24149	$1,049.74
212	$1,049.74	$0	$0.24155	$1,049.98
213	$1,049.98	$0	$0.24160	$1,050.23
214	$1,050.23	$0	$0.24166	$1,050.47
215	$1,050.47	$0	$0.24171	$1,050.71
216	$1,050.71	$0	$0.24177	$1,050.95
217	$1,050.95	$0	$0.24182	$1,051.19
218	$1,051.19	$0	$0.24188	$1,051.44
219	$1,051.44	$0	$0.24194	$1,051.68
220	$1,051.68	$0	$0.24199	$1,051.92
221	$1,051.92	$0	$0.24205	$1,052.16
222	$1,052.16	$0	$0.24210	$1,052.40
223	$1,052.40	$0	$0.24216	$1,052.65
224	$1,052.65	$0	$0.24221	$1,052.89
225	$1,052.89	$0	$0.24227	$1,053.13
226	$1,053.13	$0	$0.24233	$1,053.37
227	$1,053.37	$0	$0.24238	$1,053.61
228	$1,053.61	$0	$0.24244	$1,053.86
229	$1,053.86	$0	$0.24249	$1,054.10
230	$1,054.10	$0	$0.24255	$1,054.34
231	$1,054.34	$0	$0.24260	$1,054.58
232	$1,054.58	$0	$0.24266	$1,054.83
233	$1,054.83	$0	$0.24272	$1,055.07
234	$1,055.07	$0	$0.24277	$1,055.31
235	$1,055.31	$0	$0.24283	$1,055.56
236	$1,055.56	$0	$0.24288	$1,055.80
237	$1,055.80	$0	$0.24294	$1,056.04
238	$1,056.04	$0	$0.24300	$1,056.28
239	$1,056.28	$0	$0.24305	$1,056.53
240	$1,056.53	$0	$0.24311	$1,056.77
241	$1,056.77	$0	$0.24316	$1,057.01
242	$1,057.01	$0	$0.24322	$1,057.26
243	$1,057.26	$0	$0.24327	$1,057.50
244	$1,057.50	$0	$0.24333	$1,057.74
245	$1,057.74	$0	$0.24339	$1,057.99
246	$1,057.99	$0	$0.24344	$1,058.23
247	$1,058.23	$0	$0.24350	$1,058.47
248	$1,058.47	$0	$0.24355	$1,058.72
249	$1,058.72	$0	$0.24361	$1,058.96
250	$1,058.96	$0	$0.24367	$1,059.20
251	$1,059.20	$0	$0.24372	$1,059.45
252	$1,059.45	$0	$0.24378	$1,059.69
253	$1,059.69	$0	$0.24384	$1,059.94
254	$1,059.94	$0	$0.24389	$1,060.18
255	$1,060.18	$0	$0.24395	$1,060.42
256	$1,060.42	$0	$0.24400	$1,060.67
257	$1,060.67	$0	$0.24406	$1,060.91
258	$1,060.91	$0	$0.24412	$1,061.16
259	$1,061.16	$0	$0.24417	$1,061.40
260	$1,061.40	$0	$0.24423	$1,061.64
261	$1,061.64	$0	$0.24428	$1,061.89
262	$1,061.89	$0	$0.24434	$1,062.13
263	$1,062.13	$0	$0.24440	$1,062.38
264	$1,062.38	$0	$0.24445	$1,062.62
265	$1,062.62	$0	$0.24451	$1,062.87
266	$1,062.87	$0	$0.24457	$1,063.11
267	$1,063.11	$0	$0.24462	$1,063.36
268	$1,063.36	$0	$0.24468	$1,063.60
269	$1,063.60	$0	$0.24473	$1,063.85
270	$1,063.85	$0	$0.24479	$1,064.09
271	$1,064.09	$0	$0.24485	$1,064.33
272	$1,064.33	$0	$0.24490	$1,064.58
273	$1,064.58	$0	$0.24496	$1,064.82
274	$1,064.82	$0	$0.24502	$1,065.07
275	$1,065.07	$0	$0.24507	$1,065.31
276	$1,065.31	$0	$0.24513	$1,065.56
277	$1,065.56	$0	$0.24519	$1,065.81
278	$1,065.81	$0	$0.24524	$1,066.05
279	$1,066.05	$0	$0.24530	$1,066.30
280	$1,066.30	$0	$0.24535	$1,066.54
281	$1,066.54	$0	$0.24541	$1,066.79
282	$1,066.79	$0	$0.24547	$1,067.03
283	$1,067.03	$0	$0.24552	$1,067.28
284	$1,067.28	$0	$0.24558	$1,067.52
285	$1,067.52	$0	$0.24564	$1,067.77
286	$1,067.77	$0	$0.24569	$1,068.01
287	$1,068.01	$0	$0.24575	$1,068.26
288	$1,068.26	$0	$0.24581	$1,068.51
289	$1,068.51	$0	$0.24586	$1,068.75
290	$1,068.75	$0	$0.24592	$1,069.00
291	$1,069.00	$0	$0.24598	$1,069.24
292	$1,069.24	$0	$0.24603	$1,069.49
293	$1,069.49	$0	$0.24609	$1,069.74
294	$1,069.74	$0	$0.24615	$1,069.98
295	$1,069.98	$0	$0.24620	$1,070.23
296	$1,070.23	$0	$0.24626	$1,070.47
297	$1,070.47	$0	$0.24632	$1,070.72
298	$1,070.72	$0	$0.24637	$1,070.97
299	$1,070.97	$0	$0.24643	$1,071.21
300	$1,071.21	$0	$0.24649	$1,071.46
301	$1,071.46	$0	$0.24654	$1,071.71
302	$1,071.71	$0	$0.24660	$1,071.95
303	$1,071.95	$0	$0.24666	$1,072.20
304	$1,072.20	$0	$0.24671	$1,072.45
305	$1,072.45	$0	$0.24677	$1,072.69
306	$1,072.69	$0	$0.24683	$1,072.94
307	$1,072.94	$0	$0.24688	$1,073.19
308	$1,073.19	$0	$0.24694	$1,073.43
309	$1,073.43	$0	$0.24700	$1,073.68
310	$1,073.68	$0	$0.24705	$1,073.93
311	$1,073.93	$0	$0.24711	$1,074.17
312	$1,074.17	$0	$0.24717	$1,074.42
313	$1,074.42	$0	$0.24722	$1,074.67
314	$1,074.67	$0	$0.24728	$1,074.92
315	$1,074.92	$0	$0.24734	$1,075.16
316	$1,075.16	$0	$0.24740	$1,075.41
317	$1,075.41	$0	$0.24745	$1,075.66
318	$1,075.66	$0	$0.24751	$1,075.91
319	$1,075.91	$0	$0.24757	$1,076.15
320	$1,076.15	$0	$0.24762	$1,076.40
321	$1,076.40	$0	$0.24768	$1,076.65
322	$1,076.65	$0	$0.24774	$1,076.90
323	$1,076.90	$0	$0.24779	$1,077.14
324	$1,077.14	$0	$0.24785	$1,077.39
325	$1,077.39	$0	$0.24791	$1,077.64
326	$1,077.64	$0	$0.24797	$1,077.89
327	$1,077.89	$0	$0.24802	$1,078.14
328	$1,078.14	$0	$0.24808	$1,078.38
329	$1,078.38	$0	$0.24814	$1,078.63
330	$1,078.63	$0	$0.24819	$1,078.88
331	$1,078.88	$0	$0.24825	$1,079.13
332	$1,079.13	$0	$0.24831	$1,079.38
333	$1,079.38	$0	$0.24836	$1,079.63
334	$1,079.63	$0	$0.24842	$1,079.87
335	$1,079.87	$0	$0.24848	$1,080.12
336	$1,080.12	$0	$0.24854	$1,080.37
337	$1,080.37	$0	$0.24859	$1,080.62
338	$1,080.62	$0	$0.24865	$1,080.87
339	$1,080.87	$0	$0.24871	$1,081.12
340	$1,081.12	$0	$0.24877	$1,081.37
341	$1,081.37	$0	$0.24882	$1,081.61
342	$1,081.61	$0	$0.24888	$1,081.86
343	$1,081.86	$0	$0.24894	$1,082.11
344	$1,082.11	$0	$0.24899	$1,082.36
345	$1,082.36	$0	$0.24905	$1,082.61
346	$1,082.61	$0	$0.24911	$1,082.86
347	$1,082.86	$0	$0.24917	$1,083.11
348	$1,083.11	$0	$0.24922	$1,083.36
349	$1,083.36	$0	$0.24928	$1,083.61
350	$1,083.61	$0	$0.24934	$1,083.86
351	$1,083.86	$0	$0.24940	$1,084.11
352	$1,084.11	$0	$0.24945	$1,084.36
353	$1,084.36	$0	$0.24951	$1,084.61
354	$1,084.61	$0	$0.24957	$1,084.85
355	$1,084.85	$0	$0.24963	$1,085.10
356	$1,085.10	$0	$0.24968	$1,085.35
357	$1,085.35	$0	$0.24974	$1,085.60
358	$1,085.60	$0	$0.24980	$1,085.85
359	$1,085.85	$0	$0.24985	$1,086.10
360	$1,086.10	$0	$0.24991	$1,086.35
361	$1,086.35	$0	$0.24997	$1,086.60
362	$1,086.60	$0	$0.25003	$1,086.85
363	$1,086.85	$0	$0.25008	$1,087.10
364	$1,087.10	$0	$0.25014	$1,087.35
365	$1,087.35	$0	$0.25020	$1,087.60

ROI p.a = 8.4%

Rate of interest per day =  8.4%/365=0.023013%

Annual Return =( $ 1087.60-$ 1000)/$ 1000*100

= 8.76%

Interest Rate	Annual Return
9.3% Compounded Monthly	9.71%
9.3% Compounded Annually	9.30%
8.4% APR Daily	8.7600%

Since Our Annual Return is more at 9.3% Compounded monthly.So Investing the money at 9.3% Compounded monthly is better choice

If You have any doubts,please ask in comments

Thank you.Plese rate