A mortgage loan in the amount of $$100,000$ is made at $6$ percent interest for $20$ years. Payments are to be monthly in each part of this problem.

Required:

What will monthly payments be if

$(1)$ The loan is fully amortizing?

$(2)$ It is partially amortizing and a balloon payment of $$50,000$ is scheduled at the end of year $20?$

$(3)$ It is a non$-$amortizing, or $$interest$-$only$$ loan?

$(4)$ It is a negative amortizing loan and the loan balance will be $$150,000$ at the end of year $20?$

What will the loan balance be at the end of year $5$ under parts a $(1)$ through a $(4)?$

Assume that the lender charges $3$ points to close the loans in parts a $(1)$ through a $(4).$ What would be the APR for each?

Assuming that $3$ points are paid at closing and the $20-$year loan is prepaid at the end of year $5,$ what will be the effective rate of interest for each loan in parts a $(1)$ through a $(4)?$

Assume the loan is fully amortizing except that payments will be $$interest only$$ for the first three years $(36$ months$).$ If the loan is to fully amortize over the remaining $17$ years, what must the monthly payments be from year $4$ through year $20?$