It will take 49.8 years.
The equation for compound interest is
[tex]A=p(1+r)^t[/tex],
where A is the total amount in the account, p is the amount of principal invested, r is the interest rate as a decimal, and t is the amount of time. Substituting our information, we have:
[tex]140000=4000(1+0.074)^t
\\
\\140000=4000(1.074)^t[/tex]
Dividing both sides by 4000, we have:
[tex]\frac{140000}{4000}=\frac{4000(1.074)^t}{4000}
\\
\\35=1.074^t[/tex]
We will use logarithms to undo the exponent:
[tex]log_{1.074}35=t
\\
\\49.8=t[/tex]
