You plan to purchase a house for $$163,000$ using a $15-$year mortgage obtained from your local bank. You will make a down payment of $20$ percent of the purchase price. You will not pay off the mortgage early. Assume the homeowner will remain in the house for the full term and ignore taxes in your analysis.

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a$.$ Your bank offers you the following two options for payment. Which option should you choose?

b$.$ Your bank offers you the following two options for payment. Which option should you choose?

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a$.$ Calculate your monthly payments on this mortgage.

b$.$ Calculate the amount of interest and, separately, principal paid in the $25$th payment.

c$.$ Calculate the amount of interest and, separately, principal paid in the $120$th payment.

d$.$ Calculate the amount of interest paid over the life of this mortgage.