A new office building was constructed $5$ years

ago by a consulting engineering firm. At the

time the firm obtained the bank loan for

$10,000,000$ with a $20\%$ annual interest rate,

compounded quarterly. The terms of the loan

called for equal quarterly payments for $10-$

year period with the right of prepayment at

any time without penalty.

Due to the internal changes in the firm, it is

now proposed to refinance the loan through

an insurance company. The new loan is

planned for a $20-$year term with an interest

rate of

$24\%$ per annum, compounded quarterly. The

insurance company has a one$-$time service

charge of $5\%$ of the balance. This new loan

also calls for equal quarterly payments.

$($a$)$ What is the balance due on the original

mortgage $($principal$)$ if all payments have

been through a full five years?

$($b$)$ What will be the difference between the

equal quarterly payments in the existing

arrangement and the revised proposal?