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If you save one dollar each day and you double the amount of dollars you saved each day how much money would you have saved at the end of three months?
After 1 day you have $1
After 2 days you have $1 + $2 = $3
After 3 days you have $1 + $2 + $4 = $7
After n days you have $1 + $2 + $4 + ... + $2^(n-1) = $(2^n - 1)
The number of days in 3 months depends upon which three months are used; however, 3 months is 3/12 = 1/4 of the year. 1 year is approx 365 days, so 3 months is approx 365 ÷ 4 ≈ 91 days
So after three months you will have approx $(2^91 - 1) = $2,475,880,078,570,760,549,798,248,447 ≈ $2.476 × 10^27 or approx $2.476 octillion.
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