I would have assumed that what I needed to do is take 6% of 2475, which is $148.50, multiply that by 4 to represent the quarterly interest, which would give me $594 and then multiply that number by 10 to represent the 10 years that the CD is collecting interest, which is $5940. Then, to actually show the total in the CD I'd add the original $2475 to $5940.
Consider a simpler situation of $100 at 6% annual interest, compounded quarterly. By your method, one would compute the simple interest for the year, which would be (0.06)($100) = $6. Then one would multiply this by the four quarters to get $24 in interest.
But of course interest does not work with way. (Else, one's credit-card balances and mortgage payments would be staggeringly larger.) Instead, one does the computations at every compounding, and one does not award the full year's interest amount at every compounding. (This is why "effective" rates are always very close to the listed rates. The compoundings increase the amounts paid or owed, but only by a little over any one year's time.)
If interest is compounded twice a year, then one does the computations twice a year. Then the interest rate (let's continue to use 6%) is awarded for only half the year. To account for this halving, one uses half the interest rate: ($100)(0.06/2) = ($100)(0.03) = $3. Then, for the second half of the year, one awards the 3% interest on the new amount: ($103)(0.03) = $3.09. So the value at the end of the year will be $100 + $3 + $3.09 = $106.09.
Consider the computations in your case with the above in mind.