Answer:
To determine the implied interest rate on a Treasury bond futures contract, we need to convert the price quote (100-16) into a decimal form.
100-16 can be written as 100 + 16/32 = 100.50.
Next, we calculate the present value of the bond using the given information:
Face value of the bond (F) = $100,000
Coupon rate (C) = 6% (or 0.06)
Number of semiannual periods (n) = 20 years * 2 = 40
Discount rate (r) = Implied interest rate
Using the present value formula for a bond with semiannual payments:
PV = (C * F) / (1 + r/2)^n + F / (1 + r/2)^n
We know PV (present value) = $100.50 (the contract settlement price).
F = $100,000
C = 0.06
n = 40
Now we can solve for the implied interest rate (r) using the given information:
100.50 = (0.06 * 100,000) / (1 + r/2)^40 + 100,000 / (1 + r/2)^40
Using numerical methods or financial calculators, we can solve for the implied interest rate, which is approximately 0.0592 or 5.92%.
To calculate the contract's new value if interest rates increased by 1%, we need to adjust the implied interest rate. Adding 1% to the implied interest rate, we get 0.0592 + 0.01 = 0.0692 or 6.92%.
Using the adjusted interest rate, we can calculate the new contract value:
PV = (0.06 * 100,000) / (1 + 0.0692/2)^40 + 100,000 / (1 + 0.0692/2)^40
Again, using numerical methods or financial calculators, we can find that the new contract value is approximately $97.71.
Therefore, if interest rates increased by 1%, the contract's new value would be approximately $97.71.