Interest

What is the annual interest rate on your account if we put 32790 and after 176 days received 33939.2?

Correct result:

p =  7.3 %

Solution:

0th D .... 32790
1st D .... 32796.4183572
2nd D .... 32802.8379708
3rd D .... 32809.258841
4th D .... 32815.680968
5th D .... 32822.1043521
6th D .... 32828.5289935
7th D .... 32834.9548924
8th D .... 32841.3820492
9th D .... 32847.8104641
10th D .... 32854.2401372
11th D .... 32860.6710689
12th D .... 32867.1032594
13th D .... 32873.5367089
14th D .... 32879.9714178
15th D .... 32886.4073861
16th D .... 32892.8446143
17th D .... 32899.2831025
18th D .... 32905.7228509
19th D .... 32912.1638599
20th D .... 32918.6061297
21th D .... 32925.0496605
22th D .... 32931.4944525
23th D .... 32937.9405061
24th D .... 32944.3878214
25th D .... 32950.8363987
26th D .... 32957.2862383
27th D .... 32963.7373404
28th D .... 32970.1897052
29th D .... 32976.643333
30th D .... 32983.098224
31th D .... 32989.5543786
32th D .... 32996.0117969
33th D .... 33002.4704791
34th D .... 33008.9304256
35th D .... 33015.3916366
36th D .... 33021.8541123
37th D .... 33028.317853
38th D .... 33034.7828589
39th D .... 33041.2491302
40th D .... 33047.7166673
41th D .... 33054.1854704
42th D .... 33060.6555396
43th D .... 33067.1268753
44th D .... 33073.5994778
45th D .... 33080.0733471
46th D .... 33086.5484837
47th D .... 33093.0248878
48th D .... 33099.5025595
49th D .... 33105.9814992
50th D .... 33112.461707
51th D .... 33118.9431834
52th D .... 33125.4259284
53th D .... 33131.9099423
54th D .... 33138.3952255
55th D .... 33144.8817781
56th D .... 33151.3696003
57th D .... 33157.8586925
58th D .... 33164.3490549
59th D .... 33170.8406877
60th D .... 33177.3335912
61th D .... 33183.8277657
62th D .... 33190.3232113
63th D .... 33196.8199283
64th D .... 33203.317917
65th D .... 33209.8171777
66th D .... 33216.3177105
67th D .... 33222.8195157
68th D .... 33229.3225936
69th D .... 33235.8269444
70th D .... 33242.3325684
71th D .... 33248.8394658
72th D .... 33255.3476369
73th D .... 33261.8570819
74th D .... 33268.3678011
75th D .... 33274.8797947
76th D .... 33281.3930629
77th D .... 33287.9076061
78th D .... 33294.4234244
79th D .... 33300.9405182
80th D .... 33307.4588876
81th D .... 33313.9785329
82th D .... 33320.4994544
83th D .... 33327.0216523
84th D .... 33333.5451269
85th D .... 33340.0698783
86th D .... 33346.595907
87th D .... 33353.123213
88th D .... 33359.6517967
89th D .... 33366.1816584
90th D .... 33372.7127982
91th D .... 33379.2452164
92th D .... 33385.7789133
93th D .... 33392.313889
94th D .... 33398.850144
95th D .... 33405.3876784
96th D .... 33411.9264924
97th D .... 33418.4665863
98th D .... 33425.0079605
99th D .... 33431.550615
100th D .... 33438.0945502
101th D .... 33444.6397663
102th D .... 33451.1862636
103th D .... 33457.7340423
104th D .... 33464.2831027
105th D .... 33470.833445
106th D .... 33477.3850695
107th D .... 33483.9379763
108th D .... 33490.4921659
109th D .... 33497.0476384
110th D .... 33503.6043941
111th D .... 33510.1624332
112th D .... 33516.721756
113th D .... 33523.2823627
114th D .... 33529.8442536
115th D .... 33536.4074289
116th D .... 33542.9718889
117th D .... 33549.5376338
118th D .... 33556.104664
119th D .... 33562.6729796
120th D .... 33569.2425808
121th D .... 33575.813468
122th D .... 33582.3856414
123th D .... 33588.9591013
124th D .... 33595.5338478
125th D .... 33602.1098813
126th D .... 33608.687202
127th D .... 33615.2658101
128th D .... 33621.845706
129th D .... 33628.4268898
130th D .... 33635.0093618
131th D .... 33641.5931223
132th D .... 33648.1781715
133th D .... 33654.7645096
134th D .... 33661.352137
135th D .... 33667.9410539
136th D .... 33674.5312604
137th D .... 33681.122757
138th D .... 33687.7155438
139th D .... 33694.309621
140th D .... 33700.904989
141th D .... 33707.501648
142th D .... 33714.0995982
143th D .... 33720.6988399
144th D .... 33727.2993734
145th D .... 33733.9011988
146th D .... 33740.5043165
147th D .... 33747.1087267
148th D .... 33753.7144297
149th D .... 33760.3214256
150th D .... 33766.9297148
151th D .... 33773.5392976
152th D .... 33780.1501741
153th D .... 33786.7623446
154th D .... 33793.3758094
155th D .... 33799.9905688
156th D .... 33806.6066229
157th D .... 33813.223972
158th D .... 33819.8426165
159th D .... 33826.4625565
160th D .... 33833.0837922
161th D .... 33839.7063241
162th D .... 33846.3301522
163th D .... 33852.9552769
164th D .... 33859.5816984
165th D .... 33866.2094169
166th D .... 33872.8384328
167th D .... 33879.4687463
168th D .... 33886.1003575
169th D .... 33892.7332669
170th D .... 33899.3674746
171th D .... 33906.0029809
172th D .... 33912.639786
173th D .... 33919.2778902
174th D .... 33925.9172938
175th D .... 33932.557997
176th D .... 33939.2

 33939.2=32790q176  q=33939.232790176=1.00019574  (1+p100)=q360 p=100(q3601)=7.3% \ \\ 33939.2 = 32790 q^{ 176 } \ \\ \ \\ q = \sqrt[176]{ \dfrac{ 33939.2 }{ 32790 }} = 1.00019574 \ \\ \ \\ (1+\dfrac{p}{100}) = q^{ 360} \ \\ p= 100 (q^{ 360 } -1) = 7.3 \%



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