please help with both $117$ and $188$

$117.$ Suppose the existing loan with an interest rate of $8$ percent, outstanding balance of $$90,000$ and fixed monthly payments has $15$ years remaining on it$.$ Suppose a new loan can be offered for $15$ years at the rate of $6\mathrm{.}5$ percent to refinance the existing one. Suppose further that refinancing cost of

Real Estate Finance

$18$

the existing loan is equal to $7$ percent of its outstanding balance. Compute the implied annual savings rate for the homeowner if he goes on with the refinancing assuming the expected holding period of the borrower of $2,4,6,8,10$ and $15$ years.

$118.$ Five years ago you borrowed $$100,000$ to finance the purchase of a $$120,000$ house. The interest rate on the old mortgage is $10\%.$ Payment terms are being made monthly to amortize the loan over $30$ years. You have found another lender who will refinance the current outstanding loan balance at $8\%$ with monthly payments for $30$ years. The new lender will charge two discount points on the loan. Other refinancing costs will equal $$3,000.$

a$)$ What is the payment on the old loan?

b$)$ What is the current loan balance on the old loan $($five years after origination$)?$

c$)$ What should be the monthly payment on the new loan?

d$)$ Should vour refinance todav if the new loan is exnected to he outstanding for five vears?