The debt is amortized by equal payments made at the end of each payment interval. Compute $($a$)$ the size of the periodic payments; $($b$)$ the outstanding principal at the time indicated; $($c$)$ the interest paid by the payment following the time indicated; and $($d$)$ the principal repaid by the payment following the time indicated for finding the outstanding principal.

$\backslash$table$[[$Debt Principal,$\backslash$table$[[$Repayment$],[$Period$]],\backslash$table$[[$Payment$],[$Interval$]],$Interest Rate,$\backslash$table$[[$Conversion$],[$Period$]],\backslash$table$[[$Outstanding$],[$Principal After:$]]],[$$$13,000,8$years,$3$ months,$4\%,$quarterly,$7$th payment$]]$

$($a$)$ The size of the periodic payment is $

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$