#### Answer

It depends on the length of time. If the account is to be held for more than 16.938 years, then the account earning 6% would accrue more interest. If the account is to be held for less than 16.938 years, then the account earning 5% would accrue more interest.

#### Work Step by Step

$500*(1+(.06/4))^{4*x}$
$600*(1+.05)^x$
$500*(1+(.06/4))^{4*x}$ =$600*(1+.05)^x$
$500*(1+(.06/4))^{4*x}/500$ =$600*(1+.05)^x/500$
$(1+(.06/4))^{4*x} =1.2*(1+.05)^x$
$1.015^{4*x} =1.2*(1.05)^x$
$1.015^{4*x}/(1.05)^x =1.2*(1.05)^x/(1.05)^x$
$1.015^{4*x}/(1.05)^x = 1.2$
(A calculator was used to determine the value of x.)
$x=16.938$