When Dan signed a two$-$year contract with HardFloors Inc. as a manager, the company allowed reimbursement of $$600$ at the end of every month for his car expenses. At the time the contract was signed, money was worth $7\mathrm{.}68\%$ compounded monthly.

$($a$)$ What value did the expense reimbursement provision have when the contract was signed?

$($b$)$ What is the outstanding value of the reimbursement after the eighth payment?

A loan of $$8000$ is repaid by equal payments made at the end of every three months for two years. If interest is $7\%$ compounded quarterly, find the size of the quarterly payments, and construct an amortization schedule. Show the total paid and the total cost of the loan.

Apex Corporation borrowed $$85000$ at $8\%$ compounded quarterly for eight years to buy a warehouse. Equal payments are made at the end of every three months.

$($a$)$ Determine the size of the quarterly payments.

$($b$)$ Compute the interest included in the $16$th payment.

$($c$)$ Determine the principal repaid in the $20$th payment period.

$($d$)$ Construct a partial amortization schedule showing details of the first three payments, the last three payments, and totals.