$($Loans$)$

A loan of $10,000$ is repaid in $5$ years with quarterly payments made in arrears. The initial payment is of amount $P$ and subsequent payments increase at the end of every year by $2\%$ p$.$a$.$ compound. The interest rate is $6\%$ p$.$a$.$ effective.

$($a$)(4$ marks$)$ Find the value of $P.$

$($b$)(3$ marks$)$ What is the outstanding balance at the start of the final year?

$($c$)2$ marks$)$ What is the interest component of the first payment in the final year?