Answer: About 24 years
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Work Shown:
A = P*(1+r/n)^(n*t)
1000 = 500*(1+0.029/4)^(4*t)
1000 = 500*(1.00725)^(4*t)
1000/500 = (1.00725)^(4*t)
2 = (1.00725)^(4*t)
log(2) = log( 1.00725^(4*t) )
log(2) = 4*t*log( 1.00725 )
4*t*log( 1.00725 ) = log(2)
t = log(2)/( 4*log( 1.00725 ) )
t = 23.9881659971072 The value is approximate
t = 24 when rounding to the nearest full year
It takes approximately 24 years to double your money.