Question

Futures

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 100'16? Do not round intermediate calculations. Round your answer to two decimal places.

%??????

If interest rates increased by 1%, what would be the contract's new value? Do not round intermediate calculations. Round your answer to the nearest cent.

$ ??????

PLEASE SHOW FORMULA!! Thank you :)

Answer 1

Settlement Price = 100'16

= (100000* (100+16/32)) / 100 = 100500

Coupon is 6% Semi Annual

To calculate Implied Interest Rate

Settlement Price = coupon * ((1-(1-rate)^n)/rate)+(Face Value/(1+rate)^n)

Where

Settlement Price = 100500

Coupon is 6% Semi Annual

Face Value = 100000

Frequency is 2

Years = 20

100500 = 6000* ((1-(1-r)^20)/r)+(1000/(1+r)^20

Solving the equation we will get r = 0.0595656

or rounding off to two decimal 5.96%

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If interest rate increases by 1% so new YTM is 6.96

Now new value would be

C *(1-(1+r)^-n)/r + F/(1+r)^n

to simplify the equation

(Coupon Rate/Annual Frequency*Par Value) * (1-(1+YTM/Annual Frequency)^(-No of Times)) / (YTM/Annual Frequency) + '(Face Value)/((1+YTM/Annual Frequency)^No of Times)

or PV of Coupon + PV of Future Price

Considering rounded to two decimal r =6.96

=(6000/2)*(1-(1+(0.0696/2))^-40)/(0.0696/2)+100000/(1+(0.0696/2))^40

= 89717.69

Thanks