SOLUTION: How long does it take for an investment to double in value if it is invested at 10​% compounded monthly

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Question 1155375: How long does it take for an investment to double in value if it is invested at 10​% compounded monthly
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
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rule of 70, 7 years is estimate
P=Po(1+(.10/12))^nt
P/Po=2
2=(1+.10/12)^nt
ln both sides
ln2=nt(ln (1+.10/12)
ln2=nt*.008299
nt=83.52 months rounding at end.
t=12 because 12 compounding a year
6 years and 11 1/2 months (rounding), which is close to the 7 year estimate.

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

In this problem,  as in  ANY  OTHER  discretely compounding problem,  the answer can be
ONLY  integer number of compounding periods.


In this case,  the answer is  7  years,  which is  84  months  (84  compounding periods).

And it is  THE  EXACT  answer to this problem - not an estimate or rounding.


Again :   the  EXACT  and uniquely correct answer is  84  months = 7  years.