a$)$ Eric buys a house worth $$234600$ by paying $11\%$ down and the balance, with interest at j$52=7\mathrm{.}1\%,$ in monthly installments of $$1500$ for as long as necessary. Determine the seller's equity at the end of $4$ years.

b$)$ Sam takes out a bank loan for $$11750$ that he will repay with $11$ quarterly payments at j$12=4\mathrm{.}5\%.$ Sam has some financial troubles come up and is unable to pay the $7$th and $8$th payments. The bank allows Sam to skip these payments and then immediately after the $8$th payment the loan is refinanced at j$12=6\%.$ What is the new quarterly payment?