compound interest

Question

How long will it take for a $5000 investment to grow to $7770 at an annual rate of 9%, compounded monthly? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth. 

Answer 1

7770= 5000(1+.09/12)^12t

7770/5000= 1.0075^12t

1.554 = 1.0075^12t

take logs of both sides to the base 1.0075

12t = log_.100751.554 = ln1.554/ln1.0075

t = ln1.554/12ln1.0075

= 4.916 years

= about 4.92 years