The sales tax in California is currently 7.25 %, so when a sum of money S is spent to purchase something subject to sales tax, only 1 1.0725 ≈ 93.24 % of S goes to the seller. For example, if $ 100 is spent in a transaction, then the seller keeps $ 93.24 to spend elsewhere. When this $ 93.24 is spent, ( $ 93.24 ) 1 1.0725 ≈ $ 86.93 stays in the market to spent elsewhere, and so on. So the total amount of money spent in the "lifetime" of the initial $ 100 is 100 + 100 ( 1 1.0725 ) + 100 ( 1 1.0725 ) 2 + 100 ( 1 1.0725 ) 3 + … Find this total amount rounded to two decimal places.

The sales tax in California is currently 7.25 %, so when a sum of money S is spent to purchase something subject to sales tax, only 1 1.0725 ≈ 93.24 % of S goes to the seller. For example, if $ 100 is spent in a transaction, then the seller keeps $ 93.24 to spend elsewhere. When this $ 93.24 is spent, ( $ 93.24 ) 1 1.0725 ≈ $ 86.93 stays in the market to spent elsewhere, and so on. So the total amount of money spent in the "lifetime" of the initial $ 100 is

100 + 100 ( 1 1.0725 ) + 100 ( 1 1.0725 ) 2 + 100 ( 1 1.0725 ) 3 + …

Find this total amount rounded to two decimal places.