Please HELP me with this question!?

Question

An investment doubles in 5 years. What is the annual interest rate if the interest is compounded monthly?

Answer 1

2p = p (1+x/12)^60
2 = (1+ x/12)^60
ln 2 = ln (1+x/12)^60
ln 2= 60 ln(1+x/12)
(ln2)/60 =ln(1+x/12)
.01155 = ln(1+x/12)
e^.001155 = 1+x/12
e^.001155 -1 = x/12
x = (e^.001155 -1)812 = .0116*12 = .1394 = 13.94%

The rule of 72 would give 72/5 = 14.4%, so it's fairly close.

Answer 2

(1+x)^60 =2 where x is the monthly interest rate
60log(1+x) =log2
log(1+x)= log2/60 and (1+x)=1.0116 and the monthly rate is 1.16%
As you want the annual rate you must calculate
(1.0116)^12=1.1487 and the annual rate is 14.87%