Find the interest rate needed for an investment of $7,000 to grow to $10,500 in 6 yr if interest is compounded monthly. (Round your answer to the nearest hundredth of a percentage point.)
$\displaystyle \displaystyle\frac{A}{1+Be^{t/2}}=C$ iff
$\displaystyle A=C(1+Be^{t/2})$ and $\displaystyle 1+Be^{t/2}\ne0$.
$\displaystyle A=C(1+Be^{t/2})$ iff
$\displaystyle A=C+BCe^{t/2}$ iff
$\displaystyle A-C=BCe^{t/2}$ iff
$\displaystyle (A-C)/(BC)=e^{t/2}$ or $\displaystyle (A-C=0 and B=0)$.
$\displaystyle (A-C)/B=e^{t/2}$ iff
$\displaystyle \ln((A-C)/(BC))=t/2$.