Sheldon Blinken invented a Treasury bond index which has futures contracts traded on it. The index is composed of three bonds (A, B and C) whose current values are $101.540, $98.255 and $103.145, respectively with a par of $100. The index is calculated as the sum of the three bond values multiplied by 200. The annual coupon rates on A, B and C are 3%, 1.6%, and 5.8%, payable semi-annually. The last coupon was paid on February 1, April 1 and May 1 respectively for A, B and C. Now is July 1, 2022, and the annual risk-free rate is 2.75% (continuous compounding).

a) What must be the June-2023-futures price on the index to avoid arbitrage (maturity is June 30, 2023, 12 months from now)?

b) Is there an arbitrage opportunity if the June-2023-futures price is $60,350.45? If yes, show the transactions on one futures contract.