Step 1 :In the first quarter, the principal earns \(\frac{4.75}{100}\div4\times\$570\) in interest, so the investment is worth \(\$570 +\frac{4.75}{100}\div4\times\$570 = \left(1 + \frac{4.75}{100}\div4\right)\times\$570\).
Step 2 :Similarly, the value of the investment is multiplied by \(1 + \frac{4.75}{100}\div4\) each quarter, so after 3 years, which is \(3\times 4 = 12\) quarters, the future value is \[\left(1 + \frac{4.75}{100}\div4\right)^{3\times 4}\times\$570\approx \boxed{\$657.69}\].
Step 3 :The compound interest is the future value minus the principal, which is \[\$657.69 - \$570 = \boxed{\$87.69}\].