Question

The​ government, through a subsidy​ program, distributes ​$10000000. If each person or agency spends 55​% of what is​ received, and 55​% of this is​ spent, and so​ on, how much total increase in spending results from this goverment​ action? (Let a 1equals5500000.)

Answer 1

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,

$S = \frac{a}{1-r}$

$=\frac{0.55P}{1-0.55}$

$=\frac{0.55P}{0.45}$

$=\frac{11P}{9}$

Here, P = $ 10000000,

Therefore, total amount increase = $\frac{11\times 10000000}{9}$

$=\frac{110000000}{9}$

= $ 12,222,222.22