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Using A = P(1 + rt) and setting A = 2P and t = 10 gives r = 1/10 or 10% -- where is my math wrong?

It's exponential growth.

(1.072)*(1.072)*(1.072)*(1.072)*(1.072)*(1.072)*(1.072)*(1.072)*(1.072)*(1.072) = ~2.00

It should be A = P(1 + r)^t because of compounding.