It is now January. The current annual interest rate is $3\%.$ The June futures price for gold is $$1,246\mathrm{.}30,$ while the December futures price is $$1,251.$ Assume the June contract expires in exactly $6$ months and the December contract expires in exactly $12$ months.

Required:

a$.$ Calculate the appropriate price for December futures using the parity relationship? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Price for December futures

b$.$ Is there an arbitrage opportunity here?

Yes

N