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

Answer 1

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.