Please calculated the answer in a correct, precise, and comprehensive manner along with relevant formulas. Thanks

Question$)$ Make$-$Nu Mortgage Company is offering a new mortgage instrument called the Stable Mortgage. This mortgage is composed of both a fixed and an adjustable$-$rate component. Mrs$.$ Tiara is interested in financing a property, which costs RM$100,000,$ 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 $=1-$year Treasury$-$bill Payment reset each year Margin $=2$ percent

Interest rate cap $=$ None

Payment cap $=$ None

The projected one$-$year Treasury$-$bill index, to which the Adjustable$-$Rate Mortgage $($ARM$)$ is tied is as follows:

Beginning of Year $2=10$ percent;

Beginning of Year $3=11$ percent;

Beginning of Year $4=8$ percent;

Beginning of Year $5=12$ percent.

$($a$)$ Prepare a table that show Mrs$.$ Tiara's total monthly payment and end$-$of$-$year balances for the first $5$ years.

$($b$)$ Compute lender's yield, assuming Mrs$.$ Tiara repays the loan after five years.