At 2% compounded monthly:

2 = (1+ .02/12)^12t

log 2 = 12t*log(1.001667)

t = log 2 / 12*log(1.001667)

t = 34.69 months

= 2.89 years

At 2% compounded continuously:

2 = e^0.02t

ln2 = 0.02t

t = ln2 / 0.02

t = 34,66 months

t = 2.89 years

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