A credit union entered a lease contract valued at $\mathrm{\$}6900$. The contract provides for payments at the end of each quarter for 4 years. If interest is $5.4\mathrm{\%}$ compounded quarterly, what is the size of the quarterly payment?
The payment is $\mathrm{\$}$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：The problem is asking for the size of the quarterly payment for a lease contract. This is a problem of annuity where we need to find the periodic payment for a loan of a certain amount, given the interest rate and the number of periods.

Step 2 ：The formula for the payment of an ordinary annuity is: $P=\frac{PV}{(1-(1+r{)}^{-n})/r}$ where: $P$ is the payment, $PV$ is the present value or the total amount of the loan, $r$ is the interest rate per period, and $n$ is the number of periods.

Step 3 ：In this case, the present value $PV$ is $6900, the interest rate $r$ is 5.4% per year compounded quarterly, so the quarterly interest rate is 5.4% / 4 = 1.35% or 0.0135 in decimal form, and the number of periods $n$ is 4 years * 4 quarters = 16 quarters.

Step 4 ：Let's plug these values into the formula and calculate the payment.

Step 5 ：$PV=6900$

Step 6 ：$r=0.0135$

Step 7 ：$n=16$

Step 8 ：$P=482.39$

Step 9 ：Final Answer: The size of the quarterly payment is $\boxed{{\displaystyle \mathrm{\$}482.39}}$