Finding the time in a word problem on compound interest

Question

Suppose that $2000 is placed in a savings account at an annual rate of 8.6%, compounded semiannually. Assuming that no withdrawals are made, how long will it take for the account to grow to $3178?

Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

3178 = 2000(1+ .086/2)^2t

3178/2000 = 1.043^2t

1.589 = 1.043^2t

take logs of both sides to the base 1.043

2t = log_1.0431.589 = ln1.589/ln1.043

t = .5ln1.589/ln1.043 = .5(.4361)/

= .2316/.0421

= 5.501 years

= about 5.50 years = 5 1/2 years