Determine, to the nearest tenth of a year, how long it will take for a sum of money to double in value when it is invested at 3.1% interest, compounded every 6 months.

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The formula for compound interest is A=P(1+r/n)^(nt) where n stands for number of compounds per year. So n = 2.  P can be any starting number, A will be 2P 2P = P(1+.031/2)^(2t)    divide by P 2=(1+.031/2)^(2t)           take ln of both sides ln2 = ln((1+.031/2)^(2t))    put 2t in front as a coefficient ln2 = (2t)ln(1+.031/2)        divide both sides by 2ln(1+.031/2) (ln2)/(2ln(1+.031/2)) = t t = 22.5 years