$2.$ A $3/1$ ARM is made for $$150,000$ at $7$ percent with a $30-$year maturity.

a$.$ Assuming that fixed payments are to be made monthly for three years and that the loan is fully amortizing, what will be the monthly payments? What will be the loan balance after three years?

b$.$ What would new payments be beginning in year $4$ if the interest rate fell to $6$ percent and the loan continued to be fully amortizing?

c$.$ In $($a$)$ what would monthly payments be during year $1$ if they were interest only? What would payments be beginning in year $4$ if interest rates fell to $6$ percent and the loan became fully amortizing?

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