MakeNu Mortgage Company is offering a new mortgage instrument called the Stable Mortgage. This mortgage is composed of both a fixed rate and an adjustable rate component. Mrs$.$ Maria Perez is interested in financing a property, which costs $$140,000,$ and is to be financed by Stable Home Mortgages $($SHM$)$ on the following terms:

The SHM requires a $5$ percent down payment, costs the borrower $2$ discount points, and allows $75$ percent of the mortgage to be fixed and $25$ percent to be adjustable. The fixed portion of the loan is for $30$ years at an annual interest rate of $10\mathrm{.}5$ percent. Having neither an interest rate nor payment cap, the adjustable portion is also for $30$ years with the following terms:

Initial interest rate $=9$ percent

Index $=$ one$-$year Treasuries

Payments reset each year

Margin $=2$ percent

Interest rate cap $=$ None

Payment cap $=$ None

The projected one$-$year U$.$S$.$ Treasury$-$bill index, to which the ARM is tied, is as follows: $($BOY$)2=10$ percent; $($BOY$)3=11$ percent; $($BOY$)4=8$ percent; $($BOY$)5=12$ percent.

Required:

a$1.$ Calculate Mrs$.$ Perez$$s total monthly payments and end$-$of$-$year loan balances for the first five years.

a$2.$ Calculate the lender$$s yield, assuming Mrs$.$ Perez repays the loan after five years.

b$1.$ Calculate Mrs$.$ Perez$$s total monthly payments and end$-$of$-$year loan balances for the first five years, under the assumption that the initial interest rate is $9\mathrm{.}5$ percent and there is an annual interest rate cap of $1$ percent.

b$2.$ Calculate the lender$$s yield, assuming Mrs$.$ Perez repays the loan after five years, under the assumption that the initial interest rate is $9\mathrm{.}5$ percent and there is an annual interest rate cap of $1$ percent.