Problem $1$

You plan to purchase a $$100,000$ house using a $30-$year mortgage obtained from your local credit union. The mortgage rate offered to you is $8\mathrm{.}25\%.$ You will make a down payment of $20\%$ of the purchase price.

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 $225$th payment.