Paola is looking for a fully amortizing $30$ year Fixed Rate Mortgage with monthly payments for $$4,500,000.$ Mortgage A has a $4\mathrm{.}38\%$ interest rate and requires Paola to pay $1\mathrm{.}5$ points upfront. Mortgage B has a $6\%$ interest rate and requires Paola to pay zero fees upfront.

a$)$ Assuming Paola makes payments for six months before she sells the house and pays the bank the balance, what is Paola$$s annualized IRR from mortgage A$?$

b$)$Assuming Paola makes payments for six months before she sells the house and pays the bank the balance, what is Paola$$s annualized IRR from mortgage B$?$