he will need the mortgage at that time. Mike wants a $25-$year, fixed$-$rate mortgage in the amount of $$500,000$ with monthly payments.

Joi has agreed to lend Mike the money in three months at the current market rate of $8$ percent. Because Joi is just starting out, she does not have $$500,000$ available for the loan; so she approaches lan Turnbell, the president of IT Insurance Corporation, about purchasing the mortgage from her in three months. lan has agreed to purchase the mortgage in three months, but he is unwilling to set a price on the mortgage. Instead, he has agreed in writing to purchase the mortgage at the market rate in three months. There are Treasury bond futures contracts available for delivery in three months. A Treasury bond contract is for $$100,000$ in face value of Treasury bonds.

What is the monthly mortgage payment on Mike's mortgage $($Hint: Use time value of money you have learned to solve this problem, $PV=500,000,N=2512,\frac{1}{Y}=8\frac{\%}{12},$ CPT PMT on your BAll$+)?$

What is the most significant risk Joi faces in this deal?

How can Joi hedge this risk? Should Joe use a long hedge or short hedge?

Suppose that in the next three months the market rate of interest rises to $9$ percent. a$.$ How much will lan be willing to pay for the mortgage? $($Use the answer in #$1$ as the PMT$,$ N$=25\backslash$times $12,$ I$/$Y $=9\%/12$ CPT PV on your BAll$+)$

b$.$ What will happen to the value of Treasury bond futures contracts? Will the futures position Joe takes increase or decrease in value?

Suppose that in the next three months the market rate of interest falls to $7$ percent. a$.$ How much will lan be willing to pay for the mortgage? $($Use the answer in #$1$ as the PMT$,$ N$=25\backslash$times $12,$ I$/$Y $=7\%/12$ CPT PV on your BAll$+)$

b$.$ What will happen to the value of T$-$bond futures contracts? Will the futures position Joe takes increase or decrease in value?