9514 1404 393
Answer:
13.9 years
Explanation:
The doubling time in years for an account earning interest continuously is given exactly by the formula ...
t = 69.31472/r . . . . where r is the annual interest rate in percent
We have r = 5, so the doubling time is ...
t = 69.31472/5 = 13.8629 . . . years
It will take approximately 13.9 years for the investment to double in value.
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Additional comment
The account multiplier for continuous interest is ...
e^(rt)
That multiplier is 2 when ...
2 = e^(rt)
ln(2) = rt . . . take the natural log of both sides
t = ln(2)/r = 0.6931472/r
Multiplying by 100 so r is in percent, this is ...
t = 69.31472/r . . . . with r in percent
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This compares with the "rule of 72" that is used to estimate doubling time when interest is paid periodically. That rule would tell you doubling time at 5% is approximately 72/5 = 14.4 years. The value "72" actually depends on interest rate and frequency of compounding, so that rule only gives a crude estimate.