Consider a $30$ year, $$300,000$ fixed rate mortgage @ $7\%.$

a$.$ Holding the interest rate constant assume that fixed rate mortgages have a

$12$ year life expectancy $($approximately the expected property holding

period according to a recent NAR report$).$ Now suppose that Interest

drop to $5\%.$ Find the market value of the mortgages find the market value

of the mortgage by discounting mortgage cash flows at $5\%/$yr$.$ Assume

that the average life is unchanged at $12$ years. Repeat the valuation

exercise assuming the expected life drops to $4$ years due to increasing

prepayment $($refinancing$)$ behavior. In both cases make sure to include

the remaining principal balance in the last cash payment.

b$.$ Now suppose that the market rate rises to $9\%.$ As in part a$,$ Find the value

of the mortgage assuming a $12$ year expected life and again assuming a $15$

year life.

c$.$ Explain the results in parts a and b$.$