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Finite math

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For continuous compounding, the formula is:
A = Pert
Where A = Final amount of money, P = initial investment (principle), r = annual interest rate (expressed as a decimal value), t= time in years.  To solve for t:
ln(A) = ln(Pert) = ln(P) + ln(ert) = ln(P) + rt
ln(A) - ln(P) = rt
ln(A/P)/r = t
Plug in the values (remember r = 0.038) and solve for t.