Fractional reserve banking calculation

Today I decided to play little bit with MsExcel, and to make this little calculation.
What we have here is as following -

Mr.A1 go to his bank B1 and deposit 100 USD (EUR, BGN etc.). The bank B1 keep 10% as reserve and loan the rest 90 USD to Mr.C1, who buy something from Mr.A2,

Mr.A2 go to his bank B2 (probably different from B1) and deposit 90 USD. The bank B2 keep 10% as reserve and loan the rest 81 USD to Mr.C2, who buy something from Mr.A3,

Mr.A3 go to his bank B3 (probably different from B1 and B2) and deposit 81 USD. The bank B3 keep 10% as reserve and loan the rest 72.90 USD to Mr.C3, who buy something from Mr.A4,

...

This continue as long as the credit go to 1 USD, where we stop calculating.

From the 100 USD of Mr.A, the bank created 989.22 - 100.00 = 889.22 USD brand new money - 43 people have those money in their accounts (and 42 different people owe those 889.22 USD to the bank). This show how banks create money (and inflation too) without any money printing.

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#	Deposit USD	10% Fraction Reserve	Credit
1	100.00	10.00	90.00
2	90.00	9.00	81.00
3	81.00	8.10	72.90
4	72.90	7.29	65.61
5	65.61	6.56	59.05
6	59.05	5.90	53.14
7	53.14	5.31	47.83
8	47.83	4.78	43.05
9	43.05	4.30	38.74
10	38.74	3.87	34.87
11	34.87	3.49	31.38
12	31.38	3.14	28.24
13	28.24	2.82	25.42
14	25.42	2.54	22.88
15	22.88	2.29	20.59
16	20.59	2.06	18.53
17	18.53	1.85	16.68
18	16.68	1.67	15.01
19	15.01	1.50	13.51
20	13.51	1.35	12.16
21	12.16	1.22	10.94
22	10.94	1.09	9.85
23	9.85	0.98	8.86
24	8.86	0.89	7.98
25	7.98	0.80	7.18
26	7.18	0.72	6.46
27	6.46	0.65	5.81
28	5.81	0.58	5.23
29	5.23	0.52	4.71
30	4.71	0.47	4.24
31	4.24	0.42	3.82
32	3.82	0.38	3.43
33	3.43	0.34	3.09
34	3.09	0.31	2.78
35	2.78	0.28	2.50
36	2.50	0.25	2.25
37	2.25	0.23	2.03
38	2.03	0.20	1.82
39	1.82	0.18	1.64
40	1.64	0.16	1.48
41	1.48	0.15	1.33
42	1.33	0.13	1.20
43	1.20	0.12	1.08
	989.22	98.92	890.30