Two partners have decided to acquire a more extensive manufacturing facility. One of the partners researched and found a factory selling for $$25$ million. The partners went to a local bank to discuss the mortgage options for the factory. The bank managers provided the following offers:

Offer $1$

$30-$Year Mortgage to be repaid in equal monthly installments

No Closing costs

$5\mathrm{.}7\%$APR

Offer $2$

$20-$Year Mortgage to be repaid in equal monthly installments

No Closing Costs

Exact APR with the previous offer

The following tasks are required:

$1-$ What are the monthly payments for a $30-$year traditional mortgage? What are the payments for a $20-$year traditional mortgage?

$2-$ Prepare an amortization table for the first six months of the traditional $30-$year and $20-$year traditional Mortgage. How much of the first payment goes toward the principal? How much is the total payment for the first six months for a $30$year and $20-$year Traditional Mortgage?

$3-$ Which mortgage plan would you go with according to total payment? Explain your reasoning.