$500 principal earning 4% compounded quarterly after 6 years

The amount of interest earned would be $134.87 for a total of $634.87 after 6 years.

Explanation:
The formula for compound interest is
[tex]A=p(1+\frac{r}{n})^{tn}[/tex],

where p is the principal, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, and t is the number of years.

Our principal is $500, our interest rate is 4%=4/100=0.04, n is 4, and t is 6:
[tex]A=500(1+\frac{0.04}{4})^{4\times6} = 500(1+0.01)^{24}=500(1.01)^{24}[/tex]

Evaluating this, we get $634.87, which means there was 634.87-500 = 134.87 earned in interest.