$1)$ A borrower obtains a fully amortizing CPM loan for $$125000$ at $6\%$ interest for $10$ years. What will be the monthly payment on the loan? If this loan had a maturity of $30$ years, what would be the monthly payment?

$2)$ A fully amortizing mortgage loan is made for $$80,000$ at $6\%$ interest for $25$ years. Payments are to be made monthly

Calculate:

a$)$ Monthly payments.

b$)$ Interest and principal payment during month $1$

c$)$ Total principal and total interest paid over $25$ years.

d$)$ The outstanding loan balance if the loan is repaid at the end of year $10.$

e$)$ total monthly interest and principal payment through year $10.$

f$)$ what would the breakdown of interest and principal be during month $50?$