If there is no compounding, it will take 20 years.
The simple interest formula: Interest = Principal x rate x time
To double, the amount of interest must equal the amount of principal, so, using the formula:
4000 = 4000 x 0.05 x time
4000 = 200 x time
20 = time
However, not having compounding is unusual; if compounded:
The compound interest formula: A = P(1 + r/n)^(n·t)
A = final amount = 8000 P = principal = 4000 r = rate (as a decimal) = 0.05
n = number of times compounded per year t = time (years)
8000 = 4000(1 + 0.05/1)^(1·t)
8000 = 4000(1 + 0.05)^t
2 = (1.05)^t
log(2) = t·log(1.05
t = log(2) / log(1.05) = 14.2 years
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