Question

What is the implied interest rate on a Treasury bond ($100,000, 6% coupon, semiannual payment with 20 years to maturity) futures contract that settled at 100'12? Do not round intermediate calculations. Round your answer to two decimal places. __% If interest rates increased by 2%, what would be the contract's new value? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Face Value of Bond = $ 100000, Coupon Rate = 6 % payable semi-annually, Tenure = 20 years or (20 x 2) = 40 half-years

Let the implied interest rate be 2R%

Actual Contract Price = 100'12 or 100 +(12/32) = 100.375 % of $ 100000 = 100375 $

Semi-Annual Coupon = 0.06 x 0.5 x 100000 = $ 3000

Therefore, 100375 = 3000 x (1/R) x [1-{1/(1+R)^(40)}] + 100000 / (1+R)^(40)

Using a financial calculator/hit and trial method/ EXCEL's Goal Seek Function to solve the above equation, we get:

R = 0.02984 or 2.984 %

Implied Interest Rate = 2.984 x 2 = 5.968 %

If Interest Rates increase by 2%, then new implied interest rate = 2 + 5.968 = 7.968 %

Therefore, New Price = 3000 x (1/0.03984) x [1-{1/(1.03984)^(40)}] + 100000/(1.03984)^(40) = $ 80477.45