A savings plan requires an investor to pay $10$ installments, each one of $$500,$ due at the end of every year for $10$ years. One year after the last of such installments the bank will start making annual payments to the investor, each one for a fixed amount $P,$ for $n$ years. Assume an effective interest rate of $5\%$ p$.$a$.$

$($a$)$ If $n=7$ determine the value of $P.$

$($b$)$ If $n=,$ i$.$e$.$ payments from the bank continue indefinitely, determine the value of $P.$