Question

How long to the nearest year, will it take an investment at a rate of 12.7% to double its value if the interest is compounded every 6 months?

I keep getting 568 years, I know this is not right. Could you please show me how to do this, do I take the log of both sides or just the log of 2? thank you!

I used the A(t)= P(1+r/m)^mt
2=1(1+.127/2)^2t
log2=log1(1+.127/2)^2t
now is where I don't know where to go.

Answer 1

2=1(1+.127/2)^2t , where t is half-years (2t is years)
2 = (1+.127/2)^2t
log2=log (1+.127/2)^2t
by the rules of logs ...
log2=2t log(1+.127/2)
2t = log2/log(1.0635)
2t = 11.26

So it would take about 11 1/4 years or
11 years and 3 months