A credit union entered a lease contract valued at $ 7600. The contract provides for payments at the end of each quarter for 4 years. If interest is 6.3% compounded quarterly, what is the size of the quarterly payment?

Step 1 ：The problem is asking for the size of the quarterly payment for a lease contract. This is a problem of annuity where a sum of money (PV) is paid off over a certain period with regular payments. The formula to calculate the payment (PMT) in an ordinary annuity is: \(PMT = \frac{PV}{(1 - (1 + r)^{-n}) / r}\)

Step 2 ：Where: \(PV\) is the present value or the total amount of money that will be paid off, which is $7600 in this case. \(r\) is the interest rate per period, which is 6.3% compounded quarterly, so we divide it by 100 to convert it to decimal and by 4 because it's quarterly. \(n\) is the total number of payments, which is 4 years times 4 quarters per year.

Step 3 ：We can plug in these values into the formula to calculate the quarterly payment.

Step 4 ：Let's calculate: \(PV = 7600\), \(r = 0.01575\), \(n = 16\)

Step 5 ：Substitute the values into the formula: \(PMT = \frac{7600}{(1 - (1 + 0.01575)^{-16}) / 0.01575}\)

Step 6 ：Calculate the expression to get the final answer: \(PMT = 541.0723975424517\)

Step 7 ：\(\boxed{The size of the quarterly payment is approximately $541.07}\)