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An enterprising student invests $1,000 at an annual interest rate that will grow the original investment to $2,000 in four years. In four more years,

An enterprising student invests $1,000 at an annual interest rate that will grow the original investment to $2,000 in four years. In four more years, the initial amount will grow to
$4,000, and this pattern of doubling every four years repeats over a total time span of 36 years.
What is the magical interest rate the student is earning?
How much money will the student gain in 36 years?

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