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:

a$.$ 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" Ioan?

$(4)$ It is a negative amortizing loan and the loan

balance will be $$150,000$ at the end of year $20?$

b$.$ What will the loan balance be at the end of year $5$ under

parts a $(1)$ through a $(4)?$

c$.$ 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?

d$.$ Assuming that $3$ points are paid at closing and the $20-$year

Ioan 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

$(4)?$

e$.$ Assume the loan is fully amortizing except that payments will

be "interest only" for the first three years $(36$ months$).$ If the

Ioan is to fully amortize over the remaining $17$ years, what

must the monthly payments be from year $4$ through year

$20?$