A bank issues a $100,000 fixed-rate 30-year mortgage with a nominal annual rate of 4.5%. If the required rate drops to 4.0% immediately after the mortgage is issued, what is the impact on the value of the mortgage? Assume the bank hedged the position with a short position in two 10-year T-bond futures. The original price was 64 12/32 and expired at 67 16/32 on a $100,000 face value contract.
What was the gain on the futures? What is the total impact on the bank?