A new office building was constructed $5$ years ago by a consulting

engineering firm. At that time the firm obtained a bank loan for $

$600,000$ with a $12\%$ annual interest rate, compounded quarterly. The

loan terms call for equal quarterly payments for $10$ years. The loan

also allows for its prepayment at any time without penalty. The firm

proposes to refinance the loan through an insurance company. The

new loan would be for a $20-$ year term with an interest rate of $8\%$ per

year, compounded quarterly. The insurance company requires the

payment of a $5\%$ loan initiation charge $($often described as a $"5-$

point loan fee"$),$ which will be added to the starting balance. $($a$)$

What is the balance due on the original mortgage if $16$ payments have

been made?

$($b$)$ What is the difference between the old and new quarterly

payments?