a$)$ If the spot price of gold is $$1,500$ per troy ounce, the risk$-$free interest rate is $2\%,$ and the total

amount of storage and insurance costs are $$100,$ what should be the forward price of gold for

delivery in one year? Use an arbitrage argument to prove your answer $($hint: use an example of

forward price higher than the calculated correct price to show a successful arbitrage strategy

short$/$long and borrow or lend$)(5$ points$)$

b$)$ Show how you could make risk$-$free arbitrage profits if the forward price is $$1,550(5$ points$)$