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?
Note: The abbreviations have the following meanings
PVIFA= Present Value Interest Factor for an Annuity
They can be read from tables or calculated using the following equations
PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
If the required rate drops to 4.0% immediately after the mortgage is issued, what is the impact on the value of the mortgage?
Calculate the monthly mortgage payments:
Frequency= M Monthly
No of years= 30
No of Periods= 360
Discount rate ...
The solution calculates the gain on the futures contract that has been used for hedging a drop in interest rate.