Question

How long it will take for $300 to double when invested at 6% annual interest compounded twice a year?

Answer 1

Use the compound interest formula:
FV=PV*(1+r)^t
or
FV/PV=2=(1+r)^t
Here FV/PV=2 (double)
r=6% p.a., so 3% for 6 months.
Take log on each side and divide to solve for t:
log(2)=tlog(1+r/2)
t=log(2)/log(1.03)=23.45 periods of 6 months, or
11.72 years approx.

You can check your answer using the rule of 72, which is 72/interest rate=number of years to double. 72/6=12.
Since it is compounded every 6 months, it takes slightly less time.
If it were compounded yearly, it would have taken log(2)/log(1.06)=11.9 years.

Answer 2

thank you sooo much (:

Answer 3

You're welcome!