How long will it take an investment to double at 7% interest compounded continuously?
July 29th, 2010
How long will it take an investment to double at 7% interest compounded continuously?? I also need the same question but triple instead of double. I’m just not getting how to solve for that. Thanks!
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About 10 years. The approximate daily interest rate is r = 0.07/365.25. If n is the number of days of compounded interest, then you want (1 + r)^n = 2. Take logs to get n log(1 + r) = log 2, which implies n = log 2 / log (1 + r). Plug in the value of r above and you get n = 3617 days, which is 3617/365.25 = 9.9 years.
An approximate answer would be to use the rule of 72. Just divide the interest rate (7%) into 72 and you get about 10. It works pretty well as an approximation.
2=e^(.07t)
ln(2)=.07t
ln(2)/.07=t
t=9.9 years
so that is about 10 years
For Tripple
3=e^(.07t)
ln(3)=.07t
ln(3)/.07=t
t=15.7 years