$22.$ Mortgage Question $(20$ pts$)$You are considering purchasing a house that costs $$120,000.$ Assuming you have $$30,000$ available for a down payment and plan to borrow the remainder over $15$ years at $4\mathrm{.}20\%$ interest.a$.(10$ pts$)$ What will be your monthly mortgage payment?b$.(10$ pts$)$ After $5$ years you get a job transfer and have to sell the house. What is the payoff value of your remaining loan balance? $($hint: find PV of remaining payments$)$