Respuesta :
Answer:
$ 12,222,222.22
Step-by-step explanation:
Let P be the initial amount distributed,
Since, the spending in first instance = 55% of P
= 0.55(P)
In second instance = 55% of (0.55(P)) = 0.55² P
In third instance = 55% of (0.55² P) = 0.55³ P,
............................., so on.....
Thus, total increase in spending = 0.55P + 0.55² P + 0.55³P.....
We know that,
0.55P, 0.55²P, 0.55³P,..............
Is a GP with infinite number of terms,
Having first term, a = 0.55P,
Common ratio, r = 0.55,
Hence, the sum of the above series,
[tex]S = \frac{a}{1-r}[/tex]
[tex]=\frac{0.55P}{1-0.55}[/tex]
[tex]=\frac{0.55P}{0.45}[/tex]
[tex]=\frac{11P}{9}[/tex]
Here, P = $ 10000000,
Therefore, total amount increase = [tex]\frac{11\times 10000000}{9}[/tex]
[tex]=\frac{110000000}{9}[/tex]
= $ 12,222,222.22
