$1-$ A fully amortizing mortgage loan is made for $$80,000$ at $6$ percent interest for $25$ years. Payments are to be made monthly. Calculate:

a$.$ Monthly payments.

b$.$ Interest and principal payments 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 payments through year $10.$

$2-$ A fully amortizing mortgage loan is made for $$100,000$ at $6$ percent interest for $30$ years. Determine payments for each of the periods below if interest is accured:

a$.$ Monthly.

c$.$ Annually.

d$.$ Weekly.

$3-$ A partially amortizing mortgage is made for $$60,000$ for a term of $10$ years. The borrower and lender agree that a balance of $$20,000$ will remain and be repaid as a lump sum at that time.

a$.$ If the interest rate is $7$ percent, what must monthly payments be over the $10-$year period?

$4-$ A fully amortizing loan for $$90,000$ for $10$ years is made at $6$ percent interest. The lender and borrower agree that payments will be monthly for year $10.$ Assuming $2$ points are charged by the lender, what will be the yield if the loan is repaid at the end of year $10?$ What must the loan balance be if it is repaid after year $4?$ What will be the yield to the lender if the loan is repaid at the end of year $4?$